Journal articles: 'Trajectory generation under dynamic constraints'

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Al Younes, Younes, and Martin Barczyk. "Nonlinear Model Predictive Horizon for Optimal Trajectory Generation." Robotics 10, no. 3 (July 14, 2021): 90. http://dx.doi.org/10.3390/robotics10030090.

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This paper presents a trajectory generation method for a nonlinear system under closed-loop control (here a quadrotor drone) motivated by the Nonlinear Model Predictive Control (NMPC) method. Unlike NMPC, the proposed method employs a closed-loop system dynamics model within the optimization problem to efficiently generate reference trajectories in real time. We call this approach the Nonlinear Model Predictive Horizon (NMPH). The closed-loop model used within NMPH employs a feedback linearization control law design to decrease the nonconvexity of the optimization problem and thus achieve faster convergence. For robust trajectory planning in a dynamically changing environment, static and dynamic obstacle constraints are supported within the NMPH algorithm. Our algorithm is applied to a quadrotor system to generate optimal reference trajectories in 3D, and several simulation scenarios are provided to validate the features and evaluate the performance of the proposed methodology.

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Cisek, Paul, Stephen Grossberg, and Daniel Bullock. "A Cortico-Spinal Model of Reaching and Proprioception under Multiple Task Constraints." Journal of Cognitive Neuroscience 10, no. 4 (July 1998): 425–44. http://dx.doi.org/10.1162/089892998562852.

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A model of cortico-spinal trajectory generation for voluntary reaching movements is developed to functionally interpret a broad range of behavioral, physiological, and anatomical data. The model simulates how arm movements achieve their remarkable efficiency and accuracy in response to widely varying positional, speed, and force constraints. A key issue in arm movement control is how the brain copes with such a wide range of movement contexts. The model suggests how the brain may set automatic and volitional gating mechanisms to vary the balance of static and dynamic feedback information to guide the movement command and to compensate for external forces. For example, with increasing movement speed, the system shifts from a feedback position controller to a feedforward trajectory generator with superimposed dynamics compensation. Simulations of the model illustrate how it reproduces the effects of elastic loads on fast movements, endpoint errors in Coriolis fields, and several effects of muscle tendon vibration, including tonic and antagonist vibration reflexes, position and movement illusions, effects of obstructing the tonic vibration reflex, and reaching undershoots caused by antagonist vibration.

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Yan, Xinghui, Minchi Kuang, and Jihong Zhu. "A Geometry-Based Guidance Law to Control Impact Time and Angle under Variable Speeds." Mathematics 8, no. 6 (June 23, 2020): 1029. http://dx.doi.org/10.3390/math8061029.

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To provide a feasible solution for a variable speed unmanned aerial vehicle (UAV) to home on a target with impact time and angle constraints, this paper presents a novel geometry-based guidance law composed of trajectory reshaping and tracking. A trajectory generation process using Bezier curves is introduced to satisfy the impact time and angle constraints under time-varying speed. The impact angle is satisfied by driving the UAV along a specified ending line. The impact time is satisfied by controlling the trajectory length, which is realized through adjusting one Bezier curve end point along the ending line. The adjustable range of this end point, along with the maximum trajectory curvature, is analyzed to ensure that the trajectory is flyable. Guidance command is generated using inverse dynamics. Numerical simulations under various scenarios are demonstrated to illustrate the performance and validate the effectiveness of the proposed method.

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Karimi, J., and Seid H. Pourtakdoust. "Integrated motion planning and trajectory control system for unmanned air vehicles." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 227, no. 1 (January 6, 2012): 3–18. http://dx.doi.org/10.1177/0954410011432244.

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Motion planning and trajectory control are two basic challenges of unmanned vehicles. In motion planning problem, feasible trajectories are developed while nonlinear dynamic model and performance constraints of the vehicle under utility are considered. In this study, motion planning is performed via an enhanced particle swarm optimization algorithm. The resulting offline generated trajectories are tracked using a nonlinear trajectory control system methodology. The Lyapunov-based constrained backstepping approach and command filters are utilized in designing the trajectory control system. Command filters smoothen the input signals and provide their derivatives. Evaluation of the proposed integrated approach in several simulated scenarios has effectively demonstrated the potential of both algorithms in generating optimal contour matching trajectories as well as excellent tracking capability of the trajectory control system.

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Dutta, Praneet, Rashmi Ranjan Das, Rupali Mathur, and Deepika Rani Sona. "OPP approach for multi degree of freedom robotic arm Based on Kinematics and Dynamics of Robot." IAES International Journal of Robotics and Automation (IJRA) 4, no. 4 (December 1, 2015): 284. http://dx.doi.org/10.11591/ijra.v4i4.pp284-291.

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This paper deals with the trajectory and path generation of the industrial manipulator. The trajectory is obtained using the equations of motion and also the optimal path planning (OPP) approach under kinodynamic constraints. The optimal control problem is defined for the minimum cost function and to obtain the necessary conditions. Here we have used pontrygain’s minimum principle to obtain the limiting value of joint angle and also the joint velocity and torque. In this paper we have used the “Two degree of freedom (DOF) manipulator” for analysis and designing the optimal control for multi link and multi degree of freedom manipulator. For analysis purposes, simulation software has been used to formulate the trajectory and minimize the cost function involved.

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Pitakwatchara, Phongsaen. "Locomotion generation for a mobile manipulator by global minimization of the weighted generalized momentum." International Journal of Advanced Robotic Systems 17, no. 4 (July 1, 2020): 172988142093093. http://dx.doi.org/10.1177/1729881420930936.

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This article presents a method for generating the locomotion of a mobile manipulator that globally minimizes the weighted generalized momentum. The method utilizes the calculus of variation setting to address the problem for which the optimal trajectory may be computed by solving the initial value problem of the system of ordinary differential equations rather than the two-point boundary value problem. Online optimal trajectory may then be input to a suitable tracking controller for controlling the robot in real time. Effectively, the robot closed-loop dynamics is shaped to the optimal system such that the locomotion minimizes the difference of the weighted generalized momentum and the assigned potential energy under the constraints imposed on by the tracking task, joint angle, and actuator torque limits. Desired locomotion behaviors may be achieved by properly adjusting the weighting, spring, and damping matrices. Exploiting the induced dynamical force from the cooperative motion of the constituent linkages through the momentum minimization basis, the robot is able to outperform conventional locomotion pattern actuated by the platform solely.

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Tang, Xinmin, Yu Zhang, Ping Chen, Bo Li, and Songchen Han. "Strategic Deconfliction of 4D Trajectory and Perturbation Analysis for Air Traffic Control and Automation System." Discrete Dynamics in Nature and Society 2016 (2016): 1–18. http://dx.doi.org/10.1155/2016/7028305.

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Strategic 4D trajectory conflict-free planning is recognized as one of the core technologies of next-generation air traffic control and automation systems. To resolve potential conflicts during strategic 4D conflict-free trajectory planning, a protection-zone conflict-control model based on air traffic control separation constraints was proposed, in which relationships between expected arrival time and adjusted arrival time at conflicting waypoints for aircraft queues were built and transformed into dynamic linear equations under the definition of max-plus algebra. A method for strategic deconfliction of 4D trajectory was then proposed using two strategies: arrival time adjustment and departure time adjustment. In addition, departure time and flight duration perturbations were introduced to analyze the sensitivity of the planned strategic conflict-free 4D trajectories, and a robustness index for the conflict-free 4D trajectories was calculated. Finally, the proposed method was tested for the Shanghai air traffic control terminal area. The outcomes demonstrated that the planned strategic conflict-free 4D trajectories could avoid potential conflicts, and the slack time could be used to indicate their robustness. Complexity analysis demonstrated that deconfliction using max-plus algebra is more suitable for deconfliction of 4D trajectory with random sampling period in fix air route.

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Subrin, Kévin, Laurent Sabourin, Grigore Gogu, and Youcef Mezouar. "Performance Criteria to Evaluate a Kinematically Redundant Robotic Cell for Machining Tasks." Applied Mechanics and Materials 162 (March 2012): 413–22. http://dx.doi.org/10.4028/www.scientific.net/amm.162.413.

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Machine tools and robots have both evolved fundamentally and we can now question the abilities of new industrial robots concerning accurate task realization under high constraints. Requirements in terms of kinematic and dynamic capabilities in High Speed Machining (HSM) are increasingly demanding. To face the challenge of performance improvement, parallel and hybrid robotic architectures have emerged and a new generation of industrial serial robots with the ability to perform machining tasks has been designed. In this paper, we propose to evaluate the performance criteria of an industrial robot included in a kinematically redundant robotic cell dedicated to a machining task. Firstly, we present the constraints of the machining process (speed, accuracy etc.). We then detail the direct geometrical model and the kinematic model of a robot with closed chain in the arm and we propose a procedure for managing kinematic redundancy whilst integrating various criteria. Finally, we present the evolution of the criteria for a given trajectory in order to define the best location for a rotary table and to analyze the manipulators stiffness.

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Chen, Yang, Jianda Han, and Xingang Zhao. "Three-dimensional path planning for unmanned aerial vehicle based on linear programming." Robotica 30, no. 5 (September 15, 2011): 773–81. http://dx.doi.org/10.1017/s0263574711000993.

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SUMMARYIn this paper, an approach based on linear programming (LP) is proposed for path planning in three-dimensional space, in which an aerial vehicle is requested to pursue a target while avoiding static or dynamic obstacles. This problem is very meaningful for many aerial robots, such as unmanned aerial vehicles. First, the tasks of target-pursuit and obstacle-avoidance are modelled with linear constraints in relative coordination according to LP formulation. Then, two weighted cost functions, representing the optimal velocity resolution, are integrated into the final objective function. This resolution, defined to achieve the optimal velocity, deals with the optimization of a pair of orthogonal vectors. Some constraints, such as boundaries of the vehicle velocity, acceleration, sensor range, and flying height, are considered in this method. A number of simulations, under static and dynamic environments, are carried out to validate the performance of generating optimal trajectory in real time. Compared with ant colony optimization algorithm and genetic algorithm, our method has less parameters to tune and can achieve better performance in real-time application.

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FREY, CLEMENS. "CO-EVOLUTION OF FINITE STATE MACHINES FOR OPTIMIZATION: PROMOTION OF DEVICES WHICH SEARCH GLOBALLY." International Journal of Computational Intelligence and Applications 02, no. 01 (March 2002): 1–16. http://dx.doi.org/10.1142/s1469026802000397.

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In this work a co-evolutionary approach is used in conjunction with Genetic Programming operators in order to find certain transition rules for two-step discrete dynamical systems. This issue is similar to the well-known artificial-ant problem. We seek the dynamic system to produce a trajectory leading from given initial values to a maximum of a given spatial functional.This problem is recast into the framework of input-output relations for controllers, and the optimization is performed on program trees describing input filters and finite state machines incorporated by these controllers simultaneously. In the context of Genetic Programming there is always a set of test cases which has to be maintained for the evaluation of program trees. These test cases are subject to evolution here, too, so we employ a so-called host-parasitoid model in order to evolve optimizing dynamical systems.Reinterpreting these systems as algorithms for finding the maximum of a functional under constraints, we have derived a paradigm for the automatic generation of adapted optimization algorithms via optimal control. We provide numerical examples generated by the GP-system MathEvEco. These examples refer to key properties of the resulting strategies and they include statistical evidence showing that for this problem of system identification the co-evolutionary approach is superior to standard Genetic Programming.

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Rugescu, R. D., Cr E. Constantinescu, M. Al Barbelian, Alina Bogoi, and C. Dumitrache. "Orbital Injection Errors and Sensor Requirements for NERVA Space Launchers." Applied Mechanics and Materials 325-326 (June 2013): 813–18. http://dx.doi.org/10.4028/www.scientific.net/amm.325-326.813.

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The input module of the NERVA space launcher guidance system consisting of the inertial and sensor platform is responsible for the basic accuracy if the ascent trajectory and injection efficiency. The sample rate magnitude and data filtering along the real time trajectory are the only tools available for improving the guidance accuracy up to the level of requirements to secure admissible orbital injection error and the subsequent flight corridor during the orbital ascent. Analysis of the NERVA-1 flight telemetry flow from the onboard inertial platform raises the problem of the optimal selection of the onboard sample rate and of the rate of telemetry, which are not identical. The orbit injection errors are chosen from the orbit altitude constraints and subsequent accuracy requirements for the inertial sensors are derived. They show that the accuracy requirements are moderate and may be covered with almost conventional sensors. To improve the flight guidance accuracy the rocket motor chamber pressure and thrust are measured and observation of the preflight zero drift, recording noise and of the high level of embedded noise during both powered and coast atmospheric flight is performed. Simple filtering based on frequency Fourier analysis is delivered with conclusions regarding the intelligent algorithm enhancement that are developed and implemented on the next generation of flight research drone missiles RT-759M NERVA-2, right in preparation. The main rationale of that algorithm stands in the method of discriminating between false and true information on each measuring point immediately after the data are delivered by the sensors. Learning procedure from previous preflight recordings and from gradual accumulation of concurrent data streams subjected to FF spectral analysis are combined to improve data filtering, for immediate release to the next module of the autopilot. The rate of sampling is optimized from the analysis of the previous flight, inertial data records and test stand pressure and thrust records that show the level of noise. The behavior of the electronics under the dynamical loads of the rocket flight, involving overloads of more than 20 g-s and the level of vibration during the real flight and other sources of measuring errors are also focused in the research. During simulated work of the sensor platform the algorithm has been acceptably validated and prepared for real flight test performance. Information important for the NERVA autopilot design activity is structured through the multiple variance approach.

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Dahlin, Albin, and Yiannis Karayiannidis. "Adaptive Trajectory Generation Under Velocity Constraints Using Dynamical Movement Primitives." IEEE Control Systems Letters 4, no. 2 (April 2020): 438–43. http://dx.doi.org/10.1109/lcsys.2019.2946761.

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Lo Bianco, Corrado Guarino, and Aurelio Piazzi. "Minimum-time trajectory planning of mechanical manipulators under dynamic constraints." International Journal of Control 75, no. 13 (January 2002): 967–80. http://dx.doi.org/10.1080/00207170210156161.

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Hayward, Vincent, Laeeque Daneshmend, and Ajit Nilakantan. "Trajectory generation and control for automatic manipulation." Robotica 12, no. 2 (March 1994): 115–25. http://dx.doi.org/10.1017/s0263574700016702.

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SUMMARYA method is described to convert information available at manipulator programming level into trajectories which are suitable for tracking by a servo control system. This process generates trajectories in real time which comply with general dynamic and kinematic constraints. Tracking accuracy will depend mainly on the acceleration demand of the nominal trajectory setpoints - the actuator output demands, in particular, must remain bounded. Our scheme takes into consideration at the trajectory computation level the dynamics of the underlying system, dynamically available information acquired through sensors, and various types of constraints, such as manipulators. It has been developed in the context of a multi-manipulator programming and control system called Kali and developed at McGill University.

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Singh, S., and M. C. Leu. "Optimal Trajectory Generation for Robotic Manipulators Using Dynamic Programming." Journal of Dynamic Systems, Measurement, and Control 109, no. 2 (June 1, 1987): 88–96. http://dx.doi.org/10.1115/1.3143842.

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The problem of optimal control of robotic manipulators is dealt with in two stages: (1) optimal trajectory planning, which is performed off-line and results in the prescription of the position and velocity of each link as a function of time along a “given” path and (2) on-line trajectory tracking, during which the manipulator is guided along the planned trajectory using a feedback control algorithm. In order to obtain a general trajectory planning algorithm which could account for various constraints and performance indices, the technique of dynamic programming is adopted. It is shown that for a given path, this problem is reduced to a search over the velocity of one moving manipulator link. The design of the algorithm for optimal trajectory planning and the relevant computational issues are discussed. Simulations are performed to test the effectiveness of this method. The use of this algorithm in conjunction with an on-line controller is also presented.

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Rout, Amruta, Deepak Bbvl, and Bibhuti B. Biswal. "Optimal trajectory generation of an industrial welding robot with kinematic and dynamic constraints." Industrial Robot: the international journal of robotics research and application 47, no. 1 (October 12, 2019): 68–75. http://dx.doi.org/10.1108/ir-06-2019-0137.

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Purpose This paper aims to present an optimal trajectory planning for industrial MOTOMAN MA1440A gas metal arc welding system. A new and efficient evolutionary algorithm, enhanced multi-objective teaching learning-based optimization (EMOTLBO) method, i.e. TLBO with non-dominated sorting approach has been proposed to obtain the optimal joint trajectory for the defined weld seam path. Design/methodology/approach The joint trajectory of the welding robot need to be computed in an optimal manner for proper torch orientation, smooth travel of the robot along the weld path and for achieving higher positional accuracy. This can be achieved by limiting the kinematic and dynamic variations of the robot joints like joint jerks, squared acceleration and torque induced in the joints while travel of the robot along the weld path. Also, the robot travel should be done within minimum possible time for maintaining productivity. This leads to a multi-objective optimization problem which needs to be solved for maintaining proper orientation of the robot end effector. EMOTLBO has been proposed to obtain the Pareto front consisting of optimal solutions. The fuzzy membership function has been used to obtain the optimal solution from the Pareto front with best trade-off between objectives. Findings The proposed method has been implanted in MATLAB R2017a for simulation results. The joint positions have been used to program the robot for performing welding operation along the weld seam. From the simulation and experimental results, it can be concluded that the proposed approach can be effectively used for optimal trajectory planning of MOTOMAN MA 1440 A arc welding robot system as a very smooth and uniform weld bead has been obtained with maximum weld quality. Originality/value In this paper, a novel approach for optimal trajectory planning welding arc robot has been performed. Though trajectory planning of industrial robots has been done before, it has not been done yet for welding robot. The objectives are formulated taking in consideration of requirement of welding process like minimization of joint jerks and torques induced during welding operation due to travel of robot with the effect of arc spatter, minimization of squared acceleration for maintaining constant joint velocity and finally minimization of total travel time for maintaining productivity.

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Wang, Kun, Ke Li, Peng Chen, Qiuju Zhang, and Yi Cao. "Motion Constraints and Trajectory Planning of a Planar Active Dynamic Balancing Mechanism." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/496258.

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We propose a new solution to the active balancing issue under mechanical structural constraint. A dynamic model of the 3-DOF active balancer is established considering the limitations of the mechanical construction due to the lengths of the sliding rails. A methodology for the collision-avoidance trajectory planning is presented in addition to the normal trajectory planning to design the collision-free active balancing strategy. Numerical examples are presented to illustrate the effect of the parameter constrains as well as verify the effectiveness and necessity of trajectory planning.

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Zhao, Yong Ting, Bin Zheng, and Hong Lin Ma. "A New Method of 6-DOF Serial Robot’s Trajectory Planning under Multi-Constraints." Applied Mechanics and Materials 602-605 (August 2014): 1352–57. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.1352.

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This paper proposes a new method of 6-DOF serial robot’s trajectory planning. Ensuring to satisfy the physical constraints of space conditions, the robot’s trajectory is interpolated in the Cartesian coordinate system, and using quaternion interpolation to solve the multiple solution problem in RPY interpolation. Meanwhile, the interpolated position information is transformed into the angular displacement information of the joint coordinate system, and the joint space trajectory planning is achieved using the genetic algorithms integrated velocity, acceleration, jerk and torque and other important kinematic and dynamic constraints. In robot safety and stability, the method is better than the general approach, and it has both the ideal trajectory parameters of the global search ability and performance planning.

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Bharathi, Akilan, and Jingyan Dong. "A Smooth Trajectory Generation Algorithm for Addressing Higher-Order Dynamic Constraints in Nanopositioning Systems." Procedia Manufacturing 1 (2015): 216–25. http://dx.doi.org/10.1016/j.promfg.2015.09.006.

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Lavaei, Abolfazl, and M. A. Amiri Atashgah. "Optimal 3D trajectory generation in delivering missions under urban constraints for a flying robot." Intelligent Service Robotics 10, no. 3 (March 21, 2017): 241–56. http://dx.doi.org/10.1007/s11370-017-0225-x.

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Ozaki, Hiroaki, and Chang-jun Lin. "A Collision-Free Trajectory Generation of a Manipulator with Dynamic Constraints by Using Complex Method." Journal of the Robotics Society of Japan 15, no. 1 (1997): 139–44. http://dx.doi.org/10.7210/jrsj.15.139.

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Wei, Xing, Lei Liu, Yongji Wang, and Ye Yang. "Reentry Trajectory Optimization for a Hypersonic Vehicle Based on an Improved Adaptive Fireworks Algorithm." International Journal of Aerospace Engineering 2018 (2018): 1–17. http://dx.doi.org/10.1155/2018/8793908.

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Generation of optimal reentry trajectory for a hypersonic vehicle (HV) satisfying both boundary conditions and path constraints is a challenging task. As a relatively new swarm intelligent algorithm, an adaptive fireworks algorithm (AFWA) has exhibited promising performance on some optimization problems. However, with respect to the optimal reentry trajectory generation under constraints, the AFWA may fall into local optimum, since the individuals including fireworks and sparks are not well informed by the whole swarm. In this paper, we propose an improved AFWA to generate the optimal reentry trajectory under constraints. First, via the Chebyshev polynomial interpolation, the trajectory optimization problem with infinite dimensions is transformed to a nonlinear programming problem (NLP) with finite dimension, and the scope of angle of attack (AOA) is obtained by path constraints to reduce the difficulty of the optimization. To solve the problem, an improved AFWA with a new mutation strategy is developed, where the fireworks can learn from more individuals by the new mutation operator. This strategy significantly enhances the interactions between the fireworks and sparks and thus increases the diversity of population and improves the global search capability. Besides, a constraint-handling technique based on an adaptive penalty function and distance measure is developed to deal with multiple constraints. The numerical simulations of two reentry scenarios for HV demonstrate the validity and effectiveness of the proposed improved AFWA optimization method, when compared with other optimization methods.

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Mohamed, Haytham, Adel Moussa, Mohamed Elhabiby, and Naser El-Sheimy. "Real-Time Efficient Exploration in Unknown Dynamic Environments Using MAVs." ISPRS International Journal of Geo-Information 7, no. 11 (November 18, 2018): 450. http://dx.doi.org/10.3390/ijgi7110450.

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Micro aerial vehicles (MAVs) have been acknowledged as an influential technology for indoor search and rescue operations. The time constraint is a crucial factor in most search and rescue operations. The employed MAVs in indoor environments are characterized by short endurance flight time and limited payload weights. Hence, adding more batteries to extend the flight time is practically not feasible. Typically, most of the indoor missions’ environments might not be accessed and remain unknown. Working in such environments requires effective exploration and information gathering to save time and maximize the coverage area. Furthermore, due to the dynamism of such environments, choosing the least risky trajectory is an important task. This paper proposes a real-time active exploration technique which is capable of efficiently generating paths that minimize the vehicle’s risk and maximize the coverage area. Furthermore, it accomplishes real-time monitoring of sudden changes in the estimated map, due to the dynamic objects, by reevaluating at real-time the destination and trajectory to minimize the risk on the chosen path and simultaneously preserving the maximization of the coverage area. Ultimately, recording the implemented trajectory of the vehicle also assists in time-saving as the vehicle depends on this trajectory during the exit process. The performance of the technique is studied under static and dynamic environments and is also compared with different algorithms.

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Kumar, G. Naresh, AK Sarkar, KK Mangrulkar, and SE Talole. "Atmospheric vehicle trajectory optimization with minimum dynamic pressure constraint." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 232, no. 5 (April 30, 2017): 837–46. http://dx.doi.org/10.1177/0954410017699436.

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In this work, a trajectory optimization formulation for hypersonic boost–glide class vehicles to achieve maximum range under various in-flight and terminal constraints is proposed. While most of the published literature has considered maximum dynamic pressure as a constraint, the requirement of a certain minimum dynamic pressure has been addressed in this formulation to ensure aerodynamic controllability throughout the flight envelope for various ranges. The minimum dynamic pressure constraint is imposed as an in-flight inequality constraint and is achieved through a penalty function approach by casting it as a differential equation. Simulations are carried out, and the results are analyzed and presented to demonstrate the efficacy of the proposed formulation.

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Biagiotti, Luigi, and Claudio Melchiorri. "Trajectory generation via FIR filters: A procedure for time-optimization under kinematic and frequency constraints." Control Engineering Practice 87 (June 2019): 43–58. http://dx.doi.org/10.1016/j.conengprac.2019.03.017.

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Saab, Layale, Oscar E. Ramos, Francois Keith, Nicolas Mansard, Philippe Soueres, and Jean-Yves Fourquet. "Dynamic Whole-Body Motion Generation Under Rigid Contacts and Other Unilateral Constraints." IEEE Transactions on Robotics 29, no. 2 (April 2013): 346–62. http://dx.doi.org/10.1109/tro.2012.2234351.

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Rajendran, Pradeep, Travis Moscicki, Jared Wampler, Karl von Ellenrieder, and S. K. Gupta. "Trajectory planning for unmanned surface vehicles operating under wave-induced motion uncertainty in dynamic environments." International Journal of Advanced Robotic Systems 17, no. 6 (November 1, 2020): 172988142095894. http://dx.doi.org/10.1177/1729881420958948.

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We present a deliberative trajectory planning method to avoid collisions with traffic vessels. It also plans traversal across wavefields generated by these vessels and minimizes the risk of failure. Our method searches over a state-space consisting of pose and time. And, it produces collision-free and minimum-risk trajectory. It uses a lookup table to account for motion uncertainty and failure risk. We also present speed-up techniques to increase performance. Our wave-aware planner produces plans that (1) have shorter execution times and safer when compared to previously developed reactive planning schemes and (2) comply with user-defined wave-traversal constraints and Collision Regulations (COLREGs)

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Cariou, Christophe, Zoltan Gobor, Benjamin Seiferth, and Michel Berducat. "Mobile Robot Trajectory Planning Under Kinematic and Dynamic Constraints for Partial and Full Field Coverage." Journal of Field Robotics 34, no. 7 (May 29, 2017): 1297–312. http://dx.doi.org/10.1002/rob.21707.

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Peng, Yan, Mei Liu, Zhi Jie Tang, Shao Rong Xie, and Jun Luo. "Motion Planning of Nonholonomic Systems with Tracking Control Lyapunov Function." Applied Mechanics and Materials 44-47 (December 2010): 3992–96. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.3992.

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A common approach to motion planning of robots and vehicles involves finding suitable trajectories for the positions of each configuration variable, and then using feedback to regulate the system to these trajectories. However, when the system has less actuator than dynamical degrees of freedom, it is not always possible to do this arbitrarily. In this paper a tracking control Lyapunov function (TCLF) is proposed to guarantee that the trajectory generation is convergent and executable under nonholonomic constraint, and the simulation result conducted on surface vehicle shows its effectiveness.

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morisawa, Mitsuharu, Rafael Cisneros, Mehdi Benallegue, Iori Kumagai, Adrien Escande, and Fumio Kanehiro. "Sequential Trajectory Generation for Dynamic Multi-Contact Locomotion Synchronizing Contact." International Journal of Humanoid Robotics 17, no. 01 (January 22, 2020): 2050003. http://dx.doi.org/10.1142/s0219843620500036.

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This paper proposes a new framework to generate 3D multi-contact locomotion with low computation cost. The proposed framework consists of (a) the derivation of the prospect centroidal dynamics by introducing a force distribution ratio, where it can be represented with a formulation similar to the inverted pendulum’s one, and (b) the development of a fast computation method for generating a 3D center-of-mass (CoM) trajectory. Then (c) the ZMP reference is modified so that feasible contact wrench can be generated by a force distribution using the centroidal dynamics with the approximated friction cone. The proposed method allows to generate a trajectory sequentially and to change the locomotion parameters at any time even under variable CoM height. Then, the contact timing of each end-effector can be adjusted to synchronize with the actual contact with the environment by shortening or extending the desired duration of the support phase. This can be used to improve the robustness of the locomotion. The validity of the proposed method is confirmed by several numerical results in dynamic simulator: a CoM motion while changing the contact timing, a multi-contact locomotion considering a transition between biped and quadruped walking on an horizontal floor to move below obstacles. Finally, we also show a climbing stairs using handrail which requires dynamic changes of unilateral and bilateral contacts.

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Hou, Xihuan, Shuxiang Guo, Liwei Shi, Huiming Xing, He Yin, Zan Li, Mugen Zhou, and Debin Xia. "Improved Model Predictive-Based Underwater Trajectory Tracking Control for the Biomimetic Spherical Robot under Constraints." Applied Sciences 10, no. 22 (November 16, 2020): 8106. http://dx.doi.org/10.3390/app10228106.

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To improve the autonomy of the biomimetic sphere robot (BSR), an underwater trajectory tracking problem was studied. Considering the thrusters saturation of the BSR, an improved model predictive control (MPC) algorithm that features processing multiple constraints was designed. With the proposed algorithm, the kinematic and dynamic models of the BSR are combined in order to establish the predictive model, and a new state-space model is designed that is based on an increment of the control input. Furthermore, to avoid the infeasibility of the cost function in the MPC controller design, a new term with a slack variable is added to the objective function, which enables the constraints to be imposed as soft constraints. The simulation results illustrate that the BSR was able to track the desired trajectory accurately and stably while using the improved MPC algorithm. Furthermore, a comparison with the traditional MPC shows that the designed MPC-based increment of the control input is small. In addition, a comparative simulation using the backstepping method verifies the effectiveness of the proposed method. Unlike previous studies that only focused on the simulation validations, in this study a series of experiments were carried out that further demonstrate the effectiveness of the improved MPC for underwater trajectory tracking of the BSR. The experimental results illustrate that the improved MPC is able to drive the BSR to quickly track the reference trajectory. When compared with a traditional MPC and the backstepping method used in the experiment, the proposed MPC-based trajectory is closer to the reference trajectory.

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Park, Ill Woo, Baek Kyu Cho, and Jung Yup Kim. "A Real-Time Center of Gravity Trajectory Generation of a Biped Humanoid under Variable Reference ZMP Trajectory." Applied Mechanics and Materials 284-287 (January 2013): 1734–38. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.1734.

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This paper describes a method for generating a center of gravity trajectory of a biped humanoid robot under variable reference ZMP trajectory. A simple inverted pendulum model (SIPM) is used to calculate a center of gravity (CoG) trajectory from a reference zero moment point (ZMP) trajectory with an analytic form, which is based on the Fourier series. Fundamentally, we used a time segmentation based approach. For each segment, we defined its duration and boundary conditions, which are the key parameters of ZMP trajectory design. After designing the ZMP trajectory in each segment, we can automatically calculate the CoG trajectory by matching the boundary conditions and by calculating the coefficients between the time segments. The reference ZMP trajectory can be changed by updating the boundary conditions during walking. We successfully verified the proposed method through full-body dynamic simulations with variable step length.

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Kwon, Hyunki, Donggeun Cha, Jihoon Seong, Jinwon Lee, and Woojin Chung. "Trajectory Planner CDT-RRT* for Car-Like Mobile Robots toward Narrow and Cluttered Environments." Sensors 21, no. 14 (July 15, 2021): 4828. http://dx.doi.org/10.3390/s21144828.

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In order to achieve the safe and efficient navigation of mobile robots, it is essential to consider both the environmental geometry and kinodynamic constraints of robots. We propose a trajectory planner for car-like robots on the basis of the Dual-Tree RRT (DT-RRT). DT-RRT utilizes two tree structures in order to generate fast-growing trajectories under the kinodynamic constraints of robots. A local trajectory generator has been newly designed for car-like robots. The proposed scheme of searching a parent node enables the efficient generation of safe trajectories in cluttered environments. The presented simulation results clearly show the usefulness and the advantage of the proposed trajectory planner in various environments.

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Kang, Keeryun, and J. V. R. Prasad. "Development and Flight Test Evaluations of an Autonomous Obstacle Avoidance System for a Rotary-Wing UAV." Unmanned Systems 01, no. 01 (June 20, 2013): 3–19. http://dx.doi.org/10.1142/s2301385013500015.

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This paper presents the development and flight-testing of an obstacle avoidance system that can provide a rotary-wing unmanned aerial vehicle (UAV) the autonomous obstacle field navigation capability in uncertain environment. The system is composed of a sensor, an obstacle map generation algorithm from sensor measurements, an online path planning algorithm, and an adaptive vehicle controller. The novel approach of path planning presented in the paper is the integration of a newly developed receding horizon (RH) trajectory optimization scheme with a global path searching algorithm. The developed RH trajectory optimization scheme solves the local nonlinear trajectory optimization problem using approximated vehicle dynamics, maneuverability constraints, and terrain constraints within the finite range of the sensor. The global path searching by dynamic programming algorithm finds the shortest path to the destination to provide the initial guess to the RH trajectory optimization. The spline-based direct solver, Nonlinear Trajectory Generation (NTG), solves the RH trajectory optimization in real time and updates the solution continuously. The developed system is implemented within the Georgia Tech UAV Simulation Tool (GUST) and on the onboard computer of the Georgia Tech UAV test bed. Simulations and flight tests carried out for the benchmark scenarios and with sensor-in-the-loop flight tests demonstrated the viability of the developed system for autonomous obstacle field navigation capability of a UAV.

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Wang, Xueyun, Yifan Li, and Jingjuan Zhang. "A Novel IGC Scheme for RHV with the Capabilities of Online Aerodynamic Coefficient Estimation and Trajectory Generation." Mathematics 9, no. 2 (January 15, 2021): 172. http://dx.doi.org/10.3390/math9020172.

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A novel integrated guidance and control (IGC) scheme for a Re-entry Hypersonic Vehicle (RHV) is proposed with the capabilities of online aerodynamic coefficient estimation based on an Unscented Kalman Filter and online trajectory generation based on the Gaussian pseudospectral method. A linear quadratic regulator is adopted for trajectory tracking guidance and a second-layer sliding mode controller is designed for attitude control. The variation of lift and drag coefficients are modeled and estimated online, based on which a new trajectory can be generated. The commands of trajectory generation are set as moments of actuators and their extremums pose more constraints on the rate and acceleration of flow angles. Comprehensive simulations are conducted and comparable IGC performances with normal conditions are obtained under large aerodynamic coefficient errors according to online generated trajectory, which proves the effectiveness and advantages of the proposed IGC scheme.

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Farzadpour, Farsam, Mohammad Danesh, and Seyed M. TorkLarki. "Development of multi-phase dynamic equations for a seven-link biped robot with improved foot rotation in the double support phase." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 1 (April 17, 2014): 3–17. http://dx.doi.org/10.1177/0954406214531407.

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Gait generation plays a significant role in the quality of locomotion of legged robots. This paper presents the development of multi-phase dynamic equations and optimal trajectory generation for a seven-link planar-biped robot walking on the ground level with consideration of feet rotation in the double support phase. The main contribution of this paper is to increase the stability margin at the phase transition time for simultaneous feet rotation in double support phase by introducing a new style of feet rotation. First, the derivation of the dynamics equations, which is a challenging problem due to the existence of the holonomic constraints, is performed using the Lagrangian formulation. Then, an analytical solution to inverse kinematics is proposed to determine the angles of each joint. A multi-objective genetic algorithm-based optimization technique is proposed to obtain the key parameters in trajectory generation so that the zero moment point tracks a predefined stable trajectory and additionally minimizes the power consumption, which is subjected to actuators’ powers limitations. The effect of the hip height on the total power consumption is also investigated. The numerical simulations demonstrate the effectiveness of the proposed method.

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Zatla, Hicham, Bilal Tolbi, and Fares Bouriachi. "Optimal Reference Trajectory for a Type Xn-1Rp Underactuated Manipulator." Journal Européen des Systèmes Automatisés 54, no. 3 (June 25, 2021): 503–9. http://dx.doi.org/10.18280/jesa.540314.

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The aim of the present research is to find an optimal reference trajectory for an underactuated manipulator of type Xn-1Rp, where X is any type of joints and R is the last rotary joint, for n≥3. It is worth noting that in the case of absence of control of fully actuated manipulator, some second-order nonholonomic constraints may appear; these are known as acceleration constraints. The second-order nonholonomic constraint is a non-integrable differential equation. For this purpose, it was decided to combine two methods. The first one provides the open-loop control of the manipulator whatever the motion time is; in practice, the motion time should be minimal under the given geometric, technological, and dynamic constraints. To address this issue, a second method, based on the offline optimization approach, was used to achieve the time-optimal motion. It was revealed that the above combination gives an optimal control trajectory for an underactuated manipulator in which a reference trajectory can be utilized.

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LIN, Chang-jun, Hiroaki OZAKI, and Tetsuji SHIMOGAWA. "Comparison of Collision-Free Trajectory Generation Methods of a Manipulator with Dynamic Constraints in Consideration of Working Time." Transactions of the Japan Society of Mechanical Engineers Series C 64, no. 625 (1998): 3583–87. http://dx.doi.org/10.1299/kikaic.64.3583.

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Jiang, Gaoyang, Genfeng Liu, and Hansong Yu. "A Model Free Adaptive Scheme for Integrated Control of Civil Aircraft Trajectory and Attitude." Symmetry 13, no. 2 (February 20, 2021): 347. http://dx.doi.org/10.3390/sym13020347.

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The adaptive trajectory and attitude control is essential for the four-dimensional (4D) trajectory operation of civil aircraft in symmetric thrust flight. In this work, an integrated trajectory and attitude control scheme is proposed based on the =multi-input multi-output (MIMO) model free adaptive control (MFAC) method. First, the full-form dynamic linearization technique is adopted to build the equivalent data model of aircraft. Also, the MIMO MFAC scheme with saturation constraint is designed to achieve an accurate tracking control for a given 4D trajectory and attitude. Besides, the performance limitations of aircraft are taken into consideration, and the MIMO MFAC scheme with hard constraints is designed. In addition, to improve the simulation efficiency, a control scheme with mixed constraints, i.e., saturation and hard constraints, is further proposed. It can be seen from the simulation results that the proposed method can perform an integrated control of the aircraft 4D trajectory and attitude without precise modeling, and the control performance is better than that of the model-based control method in terms of flight altitude and yaw angle control. The integrated data-driven control scheme proposed in this paper provides a theoretical solution for the precise operation of aircraft under 4D trajectory.

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Tang, Jiayu, Xiangmin Li, Jinjin Dai, and Ning Bo. "A Case based Online Trajectory Planning Method of Autonomous Unmanned Combat Aerial Vehicles with Weapon Release Constraints." Defence Science Journal 70, no. 4 (July 13, 2020): 374–82. http://dx.doi.org/10.14429/dsj.70.15040.

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As a challenging and highly complex problem, the trajectory planning for unmanned combat aerial vehicle (UCAV) focuses on optimising flight trajectory under such constraints as kinematics and complicated battlefield environment. An online case-based trajectory planning strategy is proposed in this study to achieve rapid control variables solution of UCAV flight trajectory for the of delivery airborne guided bombs. Firstly, with an analysis of the ballistic model of airborne guided bombs, the trajectory planning model of UCAVs is established with launch acceptable region (LAR) as a terminal constraint. Secondly, a case-based planning strategy is presented, which involves four cases depending on the situation of UCAVs at the current moment. Finally, the feasibility and efficiency of the proposed planning strategy is validated by numerical simulations, and the results show that the presented strategy is suitable for UCAV performing airborne guided delivery missions in dynamic environments.

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Zhang, Yong-Bin, Tai-Yong Wang, Jing-Chuan Dong, Yang-Fan Liu, and Run-Ji Ke. "A corner smoothing method with feedrate blending for linear segments under geometric and kinematic constraints." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 234, no. 9 (April 13, 2020): 1227–45. http://dx.doi.org/10.1177/0954405420911336.

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To eliminate the disadvantages of linear interpolation and geometry-based smoothing methods, the one-step corner smoothing method with feedrate blending algorithm for linear segments is proposed in this article. In the proposed method, the variable acceleration and jerk optimization method will be first adopted to determine the dynamic performance of each linear segment for feedrate scheduling, which takes the different axial limits into consideration. Then, the feedrate scheduling method based on the S-type acceleration and deceleration algorithm is implemented to generate smooth feedrate profiles. Moreover, the feedrate blending algorithm is adopted to calculate the corner time analytically within the specified corner error and thus to generate the smooth trajectory without inserting a smooth curve at adjacent linear segments. With the presented one-step corner smoothing method, a smoother and more accurate trajectory could be generated with faster machining time. The results of simulations and machining experiments demonstrate the effectiveness of the proposed method.

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Li, Lin, Jiadong Xiao, Yanbiao Zou, and Tie Zhang. "Time-optimal path tracking for robots a numerical integration-like approach combined with an iterative learning algorithm." Industrial Robot: the international journal of robotics research and application 46, no. 6 (October 21, 2019): 763–78. http://dx.doi.org/10.1108/ir-03-2019-0063.

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Purpose The purpose of this paper is to propose a precise time-optimal path tracking approach for robots under kinematic and dynamic constraints to improve the work efficiency of robots and guarantee tracking accuracy. Design/methodology/approach In the proposed approach, the robot path is expressed by a scalar path coordinate and discretized into N points. The motion between two neighbouring points is assumed to be uniformly accelerated motion, so the time-optimal trajectory that satisfies constraints is obtained by using equations of uniformly accelerated motion instead of numerical integration. To improve dynamic model accuracy, the Coulomb and viscous friction are taken into account (while most publications neglect these effects). Furthermore, an iterative learning algorithm is designed to correct model-plant mismatch by adding an iterative compensation item into the dynamic model at each discrete point before trajectory planning. Findings An experiment shows that compared with the sequential convex log barrier method, the proposed numerical integration-like (NI-like) approach has less computation time and a smoother planning trajectory. Compared with the experimental results before iteration, the torque deviation, tracking error and trajectory execution time are reduced after 10 iterations. Originality/value As the proposed approach not only yields a time-optimal solution but also improves tracking performance, this approach can be used for any repetitive robot tasks that require more rapidity and less tracking error, such as assembly.

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Liu, Sheng, Fengji Dai, Shaobo Zhang, Yangqing Wang, and Zhenhua Wang. "Trend-aware motion planning for wheeled mobile robots operating in dynamic environments." International Journal of Advanced Robotic Systems 17, no. 4 (July 1, 2020): 172988142092529. http://dx.doi.org/10.1177/1729881420925292.

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Planning collision-free trajectories is essential for wheeled mobile robots operating in dynamic environments safely and efficiently. Most current trajectory generation methods focus on achieving optimal trajectories in static maps and considering dynamic obstacles as static depending on the precise motion estimation of the obstacles. However, in realistic applications, dealing with dynamic obstacles that have low reliable motion estimation is a common situation. Furthermore, inaccurate motion estimation leads to poor quality of motion prediction. To generate safe and smooth trajectories in such a dynamic environment, we propose a motion planning algorithm called trend-aware motion planning (TAMP) for dynamic obstacle avoidance, which combines with timed-elastic band. Instead of considering dynamic obstacles as static, our planning approach predicts the moving trends of the obstacles based on the given estimation. Subsequently, the approach generates a trajectory away from dynamic obstacles, meanwhile, avoiding the moving trends of the obstacles. To cope with multiple constraints, an optimization approach is adopted to refine the generated trajectory and minimize the cost. A comparison of our approach against other state-of-the-art methods is conducted. Results show that trajectories generated by TAMP are robust to handle the poor quality of obstacles’ motion prediction and have better efficiency and performance.

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Gupta, Gaurav, and Ashish Dutta. "Trajectory generation and step planning of a 12 DoF biped robot on uneven surface." Robotica 36, no. 7 (February 26, 2018): 945–70. http://dx.doi.org/10.1017/s0263574718000188.

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SUMMARYOne of the primary goals of biped locomotion is to generate and execute joint trajectories on a corresponding step plan that takes the robot from a start point to a goal while avoiding obstacles and consuming as little energy as possible. Past researchers have studied trajectory generation and step planning independently, mainly because optimal generation of robot gait using dynamic formulation cannot be done in real time. Also, most step-planning studies are for flat terrain guided by search heuristics. In the proposed method, a framework for generating trajectories as well as an overall step plan for navigation of a 12 degrees of freedom biped on an uneven terrain with obstacles is presented. In order to accomplish this, a dynamic model of the robot is developed and a trajectory generation program is integrated with it using gait variables. The variables are determined using a genetic algorithm based optimization program with the objective of minimizing energy consumption subject to balance and kinematic constraints of the biped. A database of these variables for various terrain angles and walking motions is used to train two neural networks, one for real-time trajectory generation and another for energy estimation. To develop a global navigation strategy, a weighted A* search is used to generate the footstep plan with energy considerations in sight. The efficacy of the approach is exhibited through simulation-based results on a variety of terrains.

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Convery, David J., and Steve Webb. "Generation of discrete beam-intensity modulation by dynamic multileaf collimation under minimum leaf separation constraints." Physics in Medicine and Biology 43, no. 9 (September 1, 1998): 2521–38. http://dx.doi.org/10.1088/0031-9155/43/9/007.

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Zhang, G. M., and S. G. Kapoor. "Dynamic Generation of Machined Surfaces, Part 2: Construction of Surface Topography." Journal of Engineering for Industry 113, no. 2 (May 1, 1991): 145–53. http://dx.doi.org/10.1115/1.2899671.

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In Part 1 of these two-part papers, a normal distribution model has been formulated to describe the random excitation system present during machining. Part 2 presents a methodology to dynamically generate the surface topography under the random excitation environment through computer simulation. The proposed methodology uses the tool vibratory motion along with the tool geometrical motion to construct the topography of a machined surface. Both experimental and simulation results confirm that when a small feed is used, the influence of the spiral trajectory of tool geometrical motion on the surface generation decays dramatically and the random excitation system, on the opposite, is strengthened playing a significant role in surface texture generation.

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Grimmell, William C., and Nageswara S. V. Rao. "On Source-Based Route Computation for Quickest Paths under Dynamic Bandwidth Constraints." International Journal of Foundations of Computer Science 14, no. 03 (June 2003): 503–23. http://dx.doi.org/10.1142/s0129054103001868.

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Routing in the newer generation of network transmission methods may be performed at various levels of the IP stack such as datagram, TCP stream, and application levels. It is important in the use of these methods to compute the routes that minimize the end-to-end delays for the specific routing mechanism. We formulate an abstract network path computation problem, the dynamic quickest path problem, to encompass a number of message forwarding mechanisms including circuit switching, Internet Protocol, and their variations. This problem deals with the transmission of a message from a source to a destination with the minimum end-to-end delay over a network with propagation delays and dynamic bandwidth constraints on the links. The available bandwidth for each link is specified as a piecewise constant function. We present for each message forwarding mechanism or mode an algorithm to compute a path with the minimum end-to-end delay for a given message size. Our algorithms with suitable network restrictions have polynomial time complexity in the size of the network and total number of segments in the bandwidth list.

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Mavrogiannis, Christoforos, and Ross A. Knepper. "Hamiltonian coordination primitives for decentralized multiagent navigation." International Journal of Robotics Research 40, no. 10-11 (August 13, 2021): 1234–54. http://dx.doi.org/10.1177/02783649211037731.

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We focus on decentralized navigation among multiple non-communicating agents in continuous domains without explicit traffic rules, such as sidewalks, hallways, or squares. Following collision-free motion in such domains requires effective mechanisms of multiagent behavior prediction. Although this prediction problem can be shown to be NP-hard, humans are often capable of solving it efficiently by leveraging sophisticated mechanisms of implicit coordination. Inspired by the human paradigm, we propose a novel topological formalism that explicitly models multiagent coordination. Our formalism features both geometric and algebraic descriptions enabling the use of standard gradient-based optimization techniques for trajectory generation but also symbolic inference over coordination strategies. In this article, we contribute (a) HCP (Hamiltonian Coordination Primitives), a novel multiagent trajectory-generation pipeline that accommodates spatiotemporal constraints formulated as symbolic topological specifications corresponding to a desired coordination strategy; (b) HCPnav, an online planning framework for decentralized collision avoidance that generates motion by following multiagent trajectory primitives corresponding to high-likelihood, low-cost coordination strategies. Through a series of challenging trajectory-generation experiments, we show that HCP outperforms a trajectory-optimization baseline in generating trajectories of desired topological specifications in terms of success rate and computational efficiency. Finally, through a variety of navigation experiments, we illustrate the efficacy of HCPnav in handling challenging multiagent navigation scenarios under homogeneous or heterogeneous agents across a series of environments of different geometry.

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Zhou, Ding, Zhenhua Yu, Yanquan Zhang, and Shunli Li. "Translational and rotational motion planning for spacecraft close proximity using sampling-based methods." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 10 (October 9, 2018): 3680–99. http://dx.doi.org/10.1177/0954410018803986.

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For autonomous spacecraft close proximity under environments containing multiple obstacles and complicated constraints, incrementally rapid planning approaches stemming from sampling-based methods are investigated in this paper. Exploring planners are separately developed for the impulsive maneuvered translation and the piecewise constant controlled rotation, which, however, is constrained by the pointing limits coupling with relative positions during the proximity. Using a cost-informed parent-connecting strategy originating from dynamic programming as well as a sweeping growth fashion balanced between tree-based and graph-based methods, an asymptotically optimal unidirectional exploration method is proposed to search energy-efficient translational trajectory without collision. As for the rotation planning, the pointing constraints are taken as virtual obstacles in the state-space augmented with time horizon planned by the translation and, accordingly, a bidirectional exploration method is developed to generate constraint-satisfied slew paths with fast convergence rate. Numerical experiments indicate that the proposed sampling-based methods can rapidly return asymptotic optimal translation trajectory and rotation path satisfying collision avoidance and sensor field-of-view constraints.

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Lu, Shaotian, Jingdong Zhao, Li Jiang, and Hong Liu. "Solving the Time-Jerk Optimal Trajectory Planning Problem of a Robot Using Augmented Lagrange Constrained Particle Swarm Optimization." Mathematical Problems in Engineering 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/1921479.

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The problem of minimum time-jerk trajectory planning for a robot is discussed in this paper. The optimal objective function is composed of two segments along the trajectory, which are the proportional to the total execution time and the proportional to the integral of the squared jerk (which denotes the derivative of the acceleration). The augmented Lagrange constrained particle swarm optimization (ALCPSO) algorithm, which combines the constrained particle swarm optimization (CPSO) with the augmented Lagrange multiplier (ALM) method, is proposed to optimize the objective function. In this algorithm, falling into a local best value can be avoided because a new particle swarm is generated per initial procedure, and the best value gained from the former generation is saved and delivered to the next generation during the iterative search procedure to enable the best value to be found more easily and more quickly. Finally, the proposed algorithm is tested on a planar 3-degree-of-freedom (DOF) robot; the simulation results show that the algorithm is effective, offering a solution to the time-jerk optimal trajectory planning problem of a robot under nonlinear constraints.

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Journal articles on the topic 'Trajectory generation under dynamic constraints'

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