Journal articles: 'Planning of trajectories'

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Tunik, Anatolii, Volodymyr Larin, Olha Sushchenko, and Svitlana Ilnytska. "On Features of Planning Trajectories for Quadrotors." Electronics and Control Systems 3, no. 69 (2021): 48–55. http://dx.doi.org/10.18372/1990-5548.69.16427.

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The paper deals with studying the process of planning trajectories during the quadrotor flight. The typical trajectories of the drone flights have been analyzed. Block diagram of the control system in the nonholonomic case and the horizontal flight is given. Comparative analysis of the most widespread trajectories is represented. The possibility to use two types of Dubins trajectory is analysed. Introducing polar coordinates for forming flight trajectories is proposed. The grounded choice of the quadrotor trajectories for different cases of the holonomic and nonholonomic closed-loop control systems was proposed. The advantages and disadvantages of the trajectories planning in each of these cases were analyzed. The Simulink models for generators of the quadrotor trajectories have been developed. The simulation results of generations of these trajectories have been represented. The possibilities of MATLAB for simulating flight trajectories are shown. The obtained results can be applied for unmanned aerial vehicles of different types.

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Brilhante, Igo, Jose Antonio Macedo, Franco Maria Nardini, Raffaele Perego, and Chiara Renso. "Planning sightseeing tours using crowdsensed trajectories." SIGSPATIAL Special 7, no. 1 (2015): 59–66. http://dx.doi.org/10.1145/2782759.2782769.

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Scales, Philip, Olivier Aycard, and Véronique Aubergé. "Planning Socially Expressive Mobile Robot Trajectories." Sensors 24, no. 11 (2024): 3533. http://dx.doi.org/10.3390/s24113533.

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Many mobile robotics applications require robots to navigate around humans who may interpret the robot’s motion in terms of social attitudes and intentions. It is essential to understand which aspects of the robot’s motion are related to such perceptions so that we may design appropriate navigation algorithms. Current works in social navigation tend to strive towards a single ideal style of motion defined with respect to concepts such as comfort, naturalness, or legibility. These algorithms cannot be configured to alter trajectory features to control the social interpretations made by humans. In this work, we firstly present logistic regression models based on perception experiments linking human perceptions to a corpus of linear velocity profiles, establishing that various trajectory features impact human social perception of the robot. Secondly, we formulate a trajectory planning problem in the form of a constrained optimization, using novel constraints that can be selectively applied to shape the trajectory such that it generates the desired social perception. We demonstrate the ability of the proposed algorithm to accurately change each of the features of the generated trajectories based on the selected constraints, enabling subtle variations in the robot’s motion to be consistently applied. By controlling the trajectories to induce different social perceptions, we provide a tool to better tailor the robot’s actions to its role and deployment context to enhance acceptability.

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Jamhour, E., and P. J. André. "Planning smooth trajectories along parametric paths." Mathematics and Computers in Simulation 41, no. 5-6 (1996): 615–26. http://dx.doi.org/10.1016/0378-4754(95)00105-0.

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Wang, Chang, and Chu Qing Zheng. "Lane Change Trajectory Planning and Simulation for Intelligent Vehicle." Advanced Materials Research 671-674 (March 2013): 2843–46. http://dx.doi.org/10.4028/www.scientific.net/amr.671-674.2843.

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Aiming at the trajectory planning problem of intelligent vehicle during lane change process, 7 polynomials lane change model was used to control vehicle. Basic model of this model was established at first, and then lane change trajectories were solved by using restriction of movement state. At last, the commonly form of lane change trajectories were obtained. Using real road duration time of lane change, lane change trajectories were simulated with MATLAB. The results shows that this model was suitable for lane change trajectories planning in different speed and it can be used for intelligent vehicle controlling.

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Maassen, A. "Planning urban energy trajectories: London and Barcelona." Proceedings of the Institution of Civil Engineers - Urban Design and Planning 163, no. 4 (2010): 185–92. http://dx.doi.org/10.1680/udap.2010.163.4.185.

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Jones, Dylan, and Geoffrey A. Hollinger. "Planning Energy-Efficient Trajectories in Strong Disturbances." IEEE Robotics and Automation Letters 2, no. 4 (2017): 2080–87. http://dx.doi.org/10.1109/lra.2017.2719760.

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Sampaio, Jorge H. B. "Planning 3D Well Trajectories Using Cubic Functions." Journal of Energy Resources Technology 128, no. 4 (2006): 257–67. http://dx.doi.org/10.1115/1.2358140.

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This work presents a mathematical method to design complex trajectories for three-dimensional (3D) wells. Three-dimensional cubic trajectories are obtained for various end conditions: free end, set end, free inclination/set azimuth, and set inclination/free azimuth. The resulting trajectories are smooth continuous functions, which better suit the expected performance of modern rotary steerable deviation tools, in particular point-the-bit and push-the-bit systems. A continuous and gradual change in path curvature and tool face results in the smoothest trajectory for 3D wells, that in turn results in lower torque, drag, and equipment wear. The degree of freedom and the associated parameters of the 3D curves express the commitment between the average curvature to the final length of the path, which can be adjusted to fit the design requirements and to optimize the trajectory. Several numerical examples illustrate the various end conditions. The paper also presents the full mathematical results (expressions for the 3D path, actual curvature, and actual tool face). The method is directly applicable to the well planning cycle as well as to automatic and manual hole steering.

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Vasile, Massimiliano, Juan Manuel Romero Martin, Luca Masi, et al. "Incremental planning of multi-gravity assist trajectories." Acta Astronautica 115 (October 2015): 407–21. http://dx.doi.org/10.1016/j.actaastro.2015.05.033.

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Szynkiewicz, W., and A. Gosiewski. "Coordinated Trajectories Planning for Two Cooperating Robots." IFAC Proceedings Volumes 27, no. 11 (1994): 123–28. http://dx.doi.org/10.1016/s1474-6670(17)47634-8.

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Nadin, Vincent, and Ana Maria Fernández-Maldonado. "Spatial planning systems in Europe: multiple trajectories." Planning Practice & Research 38, no. 5 (2023): 625–38. http://dx.doi.org/10.1080/02697459.2023.2258568.

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Ma, Chi, Da Zou, Huan Qi, et al. "A novel surgical planning system using an AI model to optimize planning of pedicle screw trajectories with highest bone mineral density and strongest pull-out force." Neurosurgical Focus 52, no. 4 (2022): E10. http://dx.doi.org/10.3171/2022.1.focus21721.

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OBJECTIVE The purpose of this study was to evaluate the ability of a novel artificial intelligence (AI) model in identifying optimized transpedicular screw trajectories with higher bone mineral density (BMD) as well as higher pull-out force (POF) in osteoporotic patients. METHODS An innovative pedicle screw trajectory planning system called Bone’s Trajectory was developed using a 3D graphic search and an AI-based finite element analysis model. The preoperative CT scans of 21 elderly osteoporotic patients were analyzed retrospectively. The AI model automatically calculated the number of alternative transpedicular trajectories, the trajectory BMD, and the estimated POF of L3–5. The highest BMD and highest POF of optimized trajectories were recorded and compared with AO standard trajectories. RESULTS The average patient age and average BMD of the vertebral bodies were 69.6 ± 7.8 years and 55.9 ± 17.1 mg/ml, respectively. On both sides of L3–5, the optimized trajectories showed significantly higher BMD and POF than the AO standard trajectories (p < 0.05). On average, the POF of optimized trajectory screws showed at least a 2.0-fold increase compared with AO trajectory screws. CONCLUSIONS The novel AI model performs well in enabling the selection of optimized transpedicular trajectories with higher BMD and POF than the AO standard trajectories.

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Minh, Vu Trieu, and John Pumwa. "Feasible Path Planning for Autonomous Vehicles." Mathematical Problems in Engineering 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/317494.

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The objective of this paper is to find feasible path planning algorithms for nonholonomic vehicles including flatness, polynomial, and symmetric polynomial trajectories subject to the real vehicle dynamical constraints. Performances of these path planning methods are simulated and compared to evaluate the more realistic and smoother generated trajectories. Results show that the symmetric polynomial algorithm provides the smoothest trajectory. Therefore, this algorithm is recommended for the development of an automatic control for autonomous vehicles.

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SON, TRAN CAO, and ENRICO PONTELLI. "Planning with preferences using logic programming." Theory and Practice of Logic Programming 6, no. 5 (2006): 559–607. http://dx.doi.org/10.1017/s1471068406002717.

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We present a declarative language, ${\cal PP}$, for the high-level specification of preferences between possible solutions (or trajectories) of a planning problem. This novel language allows users to elegantly express non-trivial, multi-dimensional preferences and priorities over such preferences. The semantics of ${\cal PP}$ allows the identification of most preferred trajectories for a given goal. We also provide an answer set programming implementation of planning problems with ${\cal PP}$ preferences.

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Oustaloup, A., B. Orsoni, P. Melchior, and H. Linarès. "Path planning by fractional differentiation." Robotica 21, no. 1 (2003): 59–69. http://dx.doi.org/10.1017/s0263574702004319.

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In path planning design, potential fields can introduce force constraints to ensure curvature continuity of trajectories and thus facilitate path-tracking design. The parametric thrift of fractional potentials permits smooth variations of the potential in function of the distance to obstacles without requiring design of geometric charge distribution. In the approach we use, the fractional order of differentiation is the risk coefficient associated to obstacles. A convex danger map towards a target and a convex geodesic distance map are defined. Real-time computation can also lead to the shortest minimum danger trajectory, or to the least dangerous of minimum length trajectories.

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Liu, Zhen, Hang Gao, Yeting Lin, and Xun Gong. "Enhancing Planning for Autonomous Driving via an Iterative Optimization Framework Incorporating Safety-Critical Trajectory Generation." Remote Sensing 16, no. 19 (2024): 3721. http://dx.doi.org/10.3390/rs16193721.

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Ensuring the safety of autonomous vehicles (AVs) in complex and high-risk traffic scenarios remains a critical unresolved challenge. Current AV planning methods exhibit limitations in generating robust driving trajectories that effectively avoid collisions, highlighting the urgent need for improved planning strategies to address these issues. This paper introduces a novel iterative optimization framework that incorporates safety-critical trajectory generation to enhance AV planning. The use of the HighD dataset, which is collected using the wide-area remote sensing capabilities of unmanned aerial vehicles (UAVs), is fundamental to the framework. Remote sensing enables large-scale real-time observation of traffic conditions, providing precise data on vehicle dynamics, road structures, and surrounding environments. To generate safety-critical trajectories, the decoder within the conditional variational auto-encoder (CVAE) is innovatively designed through a data-mechanism integration method, ensuring that these trajectories strictly adhere to vehicle kinematic constraints. Furthermore, two parallel CVAEs (Dual-CVAE) are trained collaboratively by a shared objective function to implicitly model the multi-vehicle interactions. Inspired by the concept of “learning to collide”, adversarial optimization is integrated into the Dual-CVAE (Adv. Dual-CVAE), facilitating efficient generation from normal to safety-critical trajectories. Building upon this, these generated trajectories are then incorporated into an iterative optimization framework, significantly enhancing the AV’s planning ability to avoid collisions. This framework decomposes the optimization process into stages, initially addressing normal trajectories and progressively tackling more safety-critical and collision trajectories. Finally, comparative case studies of enhancing AV planning are conducted and the simulation results demonstrate that the proposed method can efficiently enhance AV planning by generating safety-critical trajectories.

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Rădulescu, Iulia-Maria, Alexandru Boicea, Florin Rădulescu, and Daniel-Călin Popeangă. "A Lagrangian Backward Air Parcel Trajectories Clustering Framework." Water 13, no. 24 (2021): 3638. http://dx.doi.org/10.3390/w13243638.

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Many studies concerning atmosphere moisture paths use Lagrangian backward air parcel trajectories to determine the humidity sources for specific locations. Automatically grouping trajectories according to their geographical position simplifies and speeds up their analysis. In this paper, we propose a framework for clustering Lagrangian backward air parcel trajectories, from trajectory generation to cluster accuracy evaluation. We employ a novel clustering algorithm, called DenLAC, to cluster troposphere air currents trajectories. Our main contribution is representing trajectories as a one-dimensional array consisting of each trajectory’s points position vector directions. We empirically test our pipeline by employing it on several Lagrangian backward trajectories initiated from Břeclav District, Czech Republic.

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Fang, Gu, and M. W. M. G. Dissanayake. "A neural network-based method for time-optimal trajectory planning." Robotica 16, no. 2 (1998): 143–58. http://dx.doi.org/10.1017/s0263574798000484.

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Planning appropriate trajectories can significantly increase the productivity of robot systems. To plan realistic time-optimal trajectories, the robot dynamics have to be described precisely. In this paper, a neural network based algorithm for tim e-optimal trajectory planning is introduced. This method utilises neural networks for representing the inverse dynamics of the robot. As the proposed neural networks can be trained with data obtained from exciting the robot with given torque inputs, they will capture the complete dynamics of the robot system. Threfore, the trajectories generated will be mo re realistic than those obtained by using nominal dynamic equations based on nominal parameters. Time-optimal trajectories are generated for a PUMA robot to demonstrate the proposed method.

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Wang, Xincheng, Musong Lin, Lingfeng Sang, et al. "A Linear Rehabilitative Motion Planning Method with a Multi-Posture Lower-Limb Rehabilitation Robot." Sensors 24, no. 23 (2024): 7506. http://dx.doi.org/10.3390/s24237506.

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In rehabilitation, physicians plan lower-limb exercises via linear guidance. Ensuring efficacy and safety, they design patient-specific paths, carefully plotting smooth trajectories to minimize jerks. Replicating their precision in robotics is a major challenge. This study introduces a linear rehabilitation motion planning method designed for physicians to use a multi-posture lower-limb rehabilitation robot, encompassing both path and trajectory planning. By subdividing the lower limb’s action space into four distinct training sections and classifying this space, we articulate the correlation between linear trajectories and key joint rehabilitation metrics. Building upon this foundation, a rehabilitative path generation system is developed, anchored in joint rehabilitation indicators. Subsequently, high-order polynomial curves are employed to mimic the smooth continuity of traditional rehabilitation trajectories and joint motions. Furthermore, trajectory planning is refined through the resolution of a constrained quadratic optimization problem, aiming to minimize the abrupt jerks in the trajectory. The optimized trajectories derived from our experiments are compared with randomly generated trajectories, demonstrating the suitability of trajectory optimization for real-time rehabilitation trajectory planning. Additionally, we compare trajectories generated based on the two groups of joint rehabilitation indicators, indicating that the proposed path generation system effectively assists clinicians in executing efficient and precise robot-assisted rehabilitation path planning.

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Nowell, Mark, Rachel Sparks, Gergely Zombori, et al. "Comparison of computer-assisted planning and manual planning for depth electrode implantations in epilepsy." Journal of Neurosurgery 124, no. 6 (2016): 1820–28. http://dx.doi.org/10.3171/2015.6.jns15487.

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OBJECT The objective of this study was to evaluate the clinical utility of multitrajectory computer-assisted planning software (CAP) to plan stereoelectroencephalography (SEEG) electrode arrangements. METHODS A cohort of 18 patients underwent SEEG for evaluation of epilepsy at a single center between August 2013 and August 2014. Planning of electrodes was performed manually and stored using EpiNav software. CAP was developed as a planning tool in EpiNav. The user preselects a set of cerebral targets and optimized trajectory constraints, and then runs an automated search of potential scalp entry points and associated trajectories. Each trajectory is associated with metrics for a safety profile, derived from the minimal distance to vascular structures, and an efficacy profile, derived from the proportion of depth electrodes that are within or adjacent to gray matter. CAP was applied to the cerebral targets used in the cohort of 18 previous manually planned implantations to generate new multitrajectory implantation plans. A comparison was then undertaken for trajectory safety and efficacy. RESULTS CAP was applied to 166 electrode targets in 18 patients. There were significant improvements in both the safety profile and efficacy profile of trajectories generated by CAP compared with manual planning (p < 0.05). Three independent neurosurgeons assessed the feasibility of the trajectories generated by CAP, with 131 (78.9%) of 166 trajectories deemed suitable for implementation in clinical practice. CAP was performed in real time, with a median duration of 8 minutes for each patient, although this does not include the time taken for data preparation. CONCLUSIONS CAP is a promising tool to plan SEEG implantations. CAP provides feasible depth electrode arrangements, with quantitatively greater safety and efficacy profiles, and with a substantial reduction in duration of planning within the 3D multimodality framework.

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Peng, Bo, Dexin Yu, Huxing Zhou, Xue Xiao, and Chen Xie. "A Motion Planning Method for Automated Vehicles in Dynamic Traffic Scenarios." Symmetry 14, no. 2 (2022): 208. http://dx.doi.org/10.3390/sym14020208.

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We propose a motion planning method for automated vehicles (AVs) to complete driving tasks in dynamic traffic scenes. The proposed method aims to generate motion trajectories for an AV after obtaining the surrounding dynamic information and making a preliminary driving decision. The method generates a reference line by interpolating the original waypoints and generates optional trajectories with costs in a prediction interval containing three dimensions (lateral distance, time, and velocity) in the Frenet frame, and filters the optimal trajectory by a series of threshold checks. When calculating the feasibility of optional trajectories, the cost of all optional trajectories after removing obstacle interference shows obvious axisymmetric regularity concerning the reference line. Based on this regularity, we apply the constrained Simulated Annealing Algorithm (SAA) to improve the process of searching for the optimal trajectories. Experiments in three different simulated driving scenarios (speed maintaining, lane changing, and car following) show that the proposed method can efficiently generate safe and comfortable motion trajectories for AVs in dynamic environments. Compared with the method of traversing sampling points in discrete space, the improved motion planning method saves 70.23% of the computation time, and overcomes the limitation of the spatial sampling interval.

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Ozana, Stepan, Tomas Docekal, Aleksandra Kawala-Sterniuk, Jakub Mozaryn, Milos Schlegel, and Akshaya Raj. "Trajectory Planning for Mechanical Systems Based on Time-Reversal Symmetry." Symmetry 12, no. 5 (2020): 792. http://dx.doi.org/10.3390/sym12050792.

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The generation of feasible trajectories poses an eminent task in the field of control design in mechanical systems. The paper demonstrates innovative approach in trajectory planning for mechanical systems via time-reversal symmetry. It also presents two case studies: mass-spring-damper and inverted pendulum on the cart. As real systems break the time-reversal symmetry, the authors of this work propose a unique method in order to overcome this drawback. It computes a feed-forward reference control signal and state trajectories. The proposed solution enables compensation for the effects of couplings, which break the time-symmetry by a special proposed measure. The method suppresses the overall open-loop accumulated error and produces high-quality favorable control and state trajectories. Furthermore, the existence of the designed control signal and state trajectories is guaranteed if the equations of the motion have a solution in the direct flow of time.

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Bogdanovskyi, Martin, and Josef Černohorský. "Industrial Robots Trajectories Planning for Flexible Manufacturing Systems." International Journal of Modeling and Optimization 7, no. 5 (2017): 270–74. http://dx.doi.org/10.7763/ijmo.2017.v7.596.

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Ellekilde, Lars-Peter, and Henrik Gordon Petersen. "Motion planning efficient trajectories for industrial bin-picking." International Journal of Robotics Research 32, no. 9-10 (2013): 991–1004. http://dx.doi.org/10.1177/0278364913487237.

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Sahar, Gideon, and John M. Hollerbach. "Planning of Minimum- Time Trajectories for Robot Arms." International Journal of Robotics Research 5, no. 3 (1986): 90–100. http://dx.doi.org/10.1177/027836498600500305.

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YAMAMOTO, Motoji, Takumi INOUE, and Akira MOURI. "Planning of near-minimum time trajectories for manipulators." Transactions of the Japan Society of Mechanical Engineers Series C 55, no. 516 (1989): 2077–82. http://dx.doi.org/10.1299/kikaic.55.2077.

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Bockisch, Christopher J., and Thomas Haslwanter. "Vestibular contribution to the planning of reach trajectories." Experimental Brain Research 182, no. 3 (2007): 387–97. http://dx.doi.org/10.1007/s00221-007-0997-x.

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Fasching, M. M., F. B. Prinz, and L. E. Weiss. "Planning robotic trajectories for thermal spray shape deposition." Journal of Thermal Spray Technology 2, no. 1 (1993): 45–57. http://dx.doi.org/10.1007/bf02647423.

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David, Jennifer, and Rafael Valencia. "Simultaneous Path Planning and Task Allocation in Dynamic Environments." Robotics 14, no. 2 (2025): 17. https://doi.org/10.3390/robotics14020017.

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This paper addresses the challenge of coordinating task allocation and generating collision-free trajectories for a fleet of mobile robots in dynamic environments. Our approach introduces an integrated framework comprising a centralized task allocation system and a distributed trajectory planner. The centralized task allocation system, employing a heuristic approach, aims to minimize the maximum spatial cost among the slowest robots. Tasks and trajectories are continuously refined using a distributed version of CHOMP (Covariant Hamiltonian Optimization for Motion Planning), tailored for multiple-wheeled mobile robots where the spatial costs are derived from a high-level global path planner. By employing this combined methodology, we are able to achieve near-optimal solutions and collision-free trajectories with computational performance for up to 50 robots within seconds.

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Ozaki, Hiroaki, and Chang-jun Lin. "Collision-Free Trajectory Planning for a Two-Dimensional Mobile Robot by Optimizing Continuous Curves." Journal of Robotics and Mechatronics 10, no. 4 (1998): 364–69. http://dx.doi.org/10.20965/jrm.1998.p0364.

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We propose a new algorithm for planning collision-free trajectories for a mobile robot. The trajectories of the mobile robot are described by uniform B-spline curves and these control points are optimized using the complex method. The complex method is very effective for this type of optimization of nonlinear problems because it does not require any computation of the gradient of performance index. B-spline curves have advantages for trajectory generation in that they guarantee the continuity of trajectories and the order of trajectories can be changed easily. Effectiveness is also confirmed by trajectory planning simulation of a two-dimensional mobile robot.

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Foehn, Philipp, Angel Romero, and Davide Scaramuzza. "Time-optimal planning for quadrotor waypoint flight." Science Robotics 6, no. 56 (2021): eabh1221. http://dx.doi.org/10.1126/scirobotics.abh1221.

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Quadrotors are among the most agile flying robots. However, planning time-optimal trajectories at the actuation limit through multiple waypoints remains an open problem. This is crucial for applications such as inspection, delivery, search and rescue, and drone racing. Early works used polynomial trajectory formulations, which do not exploit the full actuator potential because of their inherent smoothness. Recent works resorted to numerical optimization but require waypoints to be allocated as costs or constraints at specific discrete times. However, this time allocation is a priori unknown and renders previous works incapable of producing truly time-optimal trajectories. To generate truly time-optimal trajectories, we propose a solution to the time allocation problem while exploiting the full quadrotor’s actuator potential. We achieve this by introducing a formulation of progress along the trajectory, which enables the simultaneous optimization of the time allocation and the trajectory itself. We compare our method against related approaches and validate it in real-world flights in one of the world’s largest motion-capture systems, where we outperform human expert drone pilots in a drone-racing task.

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Pigeon, Pascale, Simone B. Bortolami, Paul DiZio, and James R. Lackner. "Coordinated Turn-and-Reach Movements. II. Planning in an External Frame of Reference." Journal of Neurophysiology 89, no. 1 (2003): 290–303. http://dx.doi.org/10.1152/jn.00160.2001.

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The preceding study demonstrated that normal subjects compensate for the additional interaction torques generated when a reaching movement is made during voluntary trunk rotation. The present paper assesses the influence of trunk rotation on finger trajectories and on interjoint coordination and determines whether simultaneous turn-and-reach movements are most simply described relative to a trunk-based or an external reference frame. Subjects reached to targets requiring different extents of arm joint and trunk rotation at a natural pace and quickly in normal lighting and in total darkness. We first examined whether the larger interaction torques generated during rapid turn-and-reach movements perturb finger trajectories and interjoint coordination and whether visual feedback plays a role in compensating for these torques. These issues were addressed using generalized Procrustes analysis (GPA), which attempts to overlap a group of configurations (e.g., joint trajectories) through translations and rotations in multi-dimensional space. We first used GPA to identify the mean intrinsic patterns of finger and joint trajectories (i.e., their average shape irrespective of location and orientation variability in the external and joint workspaces) from turn-and-reach movements performed in each experimental condition and then calculated their curvatures. We then quantified the discrepancy between each finger or joint trajectory and the intrinsic pattern both after GPA was applied individually to trajectories from a pair of experimental conditions and after GPA was applied to the same trajectories pooled together. For several subjects, joint trajectories but not finger trajectories were more curved in fast than slow movements. The curvature of both joint and finger trajectories of turn-and-reach movements was relatively unaffected by the vision conditions. Pooling across speed conditions significantly increased the discrepancy between joint but not finger trajectories for most subjects, indicating that subjects used different patterns of interjoint coordination in slow and fast movements while nevertheless preserving the shape of their finger trajectory. Higher movement speeds did not disrupt the arm joint rotations despite the larger interaction torques generated. Rather, subjects used the redundant degrees of freedom of the arm/trunk system to achieve similar finger trajectories with differing joint configurations. We examined finger movement patterns and velocity profiles to determine the frame of reference in which turn-and-reach movements could be most simply described. Finger trajectories of turn-and-reach movements had much larger curvatures and their velocity profiles were less smooth and less bell-like in trunk-based coordinates than in external coordinates. Taken together, these results support the conclusion that turn-and-reach movements are controlled in an external frame of reference.

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Su, Hai-Jun, Peter Dietmaier, and J. Michael McCarthy. "Trajectory Planning for Constrained Parallel Manipulators." Journal of Mechanical Design 125, no. 4 (2003): 709–16. http://dx.doi.org/10.1115/1.1623187.

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This paper presents an algorithm for generating trajectories for multi-degree of freedom spatial linkages, termed constrained parallel manipulators. These articulated systems are formed by supporting a workpiece, or end-effector, with a set of serial chains, each of which imposes a constraint on the end-effector. Our goal is to plan trajectories for systems that have workspaces ranging from two through five degrees-of-freedom. This is done by specifying a goal trajectory and finding the system trajectory that comes closest to it using a dual quaternion metric. We enumerate these parallel mechanisms and formulate a general numerical approach for their analysis and trajectory planning. Examples are provided to illustrate the results.

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Ogawa, Naoko, Hiromasa Oku, Koichi Hashimoto, and Masatoshi Ishikawa. "Trajectory Planning of Motile Cell for Microrobotic Applications." Journal of Robotics and Mechatronics 19, no. 2 (2007): 190–97. http://dx.doi.org/10.20965/jrm.2007.p0190.

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Our goal is to use motile microorganisms as smart microscale robots for a variety of applications. As a first step, we have achieved microrobotic control of Paramecium cell movement using galvanotaxis (locomotor response to electrical stimulus). Previous studies based on simple empirical rules that did not consider cell dynamics had only limited control. To control cells more precisely as microrobots, we must deal with Paramecium cells in the standard robotics framework. This paper is, to our knowledge, the first attempt in trajectory planning of Paramecium cells under an electric field using a dynamics model for microrobotic applications. Based on the original dynamics model, we propose trajectory planning for cells using a common well-known Lyapunov-like approach and generate cusp-free trajectories. We discuss how to generate stable streamlined trajectories for living cells in a step toward actual control. Numerical experiments demonstrate the successful stable convergence of cell trajectories to the desired location and attitude, which should prove useful in the advanced guidance of cells.

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Elnagar, Ashraf, and Anup Basu. "Piecewise smooth and safe trajectory planning." Robotica 12, no. 4 (1994): 299–307. http://dx.doi.org/10.1017/s026357470001732x.

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SUMMARYA new approach to generating smooth piecewise local trajectories for mobile robots is proposed in this paper. Given the configurations (position and direction) of two points, we search for the trajectory that minimizes the integral of acceleration (tangential and normal). The resulting trajectory should not only be smooth but also safe in order to be applicable in real-life situations. Therefore, we investigate two different obstacle-avoidance constraints that satisfy the minimization problem. Unfortunately, in this case the problem becomes more complex and not suitable for real time implementations. Therefore, we introduce two simple solutions, based on the idea of polynomial fitting, to generate safe trajectories once a collision is detected with the original smooth trajectory. Simulation results of the different algorithms are presented.

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Suzuki, Yumiko, Simon Thompson, and Satoshi Kagami. "Smooth Path Planning with Pedestrian Avoidance for Wheeled Robots." Journal of Robotics and Mechatronics 22, no. 1 (2010): 21–27. http://dx.doi.org/10.20965/jrm.2010.p0021.

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In studying smooth robot path planning with predesigned steering sets including three trajectory types, path planning with a steering set was used to generate trajectories with smooth directional changes. To put path planning to practical use in dynamic environments, robots must be more quickly motion and efficiently, without, for example, endangering pedestrians. Assuming that the trajectories of moving obstacles are predictable, smooth path planning worked in the presence ofmoving obstacles. We defined new path evaluation method suitable for wheeled robots, evaluating our planner experimentally in an office, confirmed the efficiency of our planning.

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Kyrylovych, Valerii, Petro Melnychuk, Lubomir Dimitrov, and Ilona Kryzanivska. "Automated planning of the optimal movement trajectories of mobile mechatronic devices." Scientific journal of the Ternopil national technical university 102, no. 2 (2021): 64–77. http://dx.doi.org/10.33108/visnyk_tntu2021.02.064.

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The compatible work is considered and the obtained results of the known algorithms generating unobstructed trajectories of different length and smoothness are investigated. Their operation is performed within the framework of the developed software product LSTr. The use of the analyzed set of these algorithms on the set of considered sections of the generated trajectories according to the obtained results allows a differentiated approach to the use of different algorithms on different sections of trajectories, determined by the accepted criteria of length and / or smoothness. The scientific novelty of the work and its practical significance in this area of research are determined.

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Wang, Jihe, Dexin Zhang, GuoZhong Chen, and Xiaowei Shao. "A new fuel-balanced formation keeping reference trajectories planning method." Aircraft Engineering and Aerospace Technology 90, no. 6 (2018): 927–36. http://dx.doi.org/10.1108/aeat-03-2017-0084.

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Purpose The purpose of this paper is to propose a new fuel-balanced formation keeping reference trajectories planning method based on selecting the virtual reference center(VRC) in a fuel-balanced sense in terms of relative eccentricity and inclination vectors (E/I vectors). Design/methodology/approach By using the geometrical intuitive relative E/I vectors theory, the fuel-balanced VRC selection problem is reformulated as the geometrical problem to find the optimal point to equalize the distances between the VRC and the points determined by the relative E/I vectors of satellites in relative E/I vectors plane, which is solved by nonlinear programming method. Findings Numerical simulations demonstrate that the new proposed fuel-balanced formation keeping strategy is valid, and the new method achieves better fuel-balanced performance than the traditional method, which keeps formation with respect to geometrical formation center. Research limitations/implications The new fuel-balanced formation keeping reference trajectories planning method is valid for formation flying mission whose member satellite is in circular or near circular orbit in J2 perturbed orbit environment. Practical implications The new fuel-balanced formation keeping reference trajectories planning method can be used to solve formation flying keeping problem, which involves multiple satellites in the formation. Originality/value The fuel-balanced reference trajectories planning problem is reformulated as a geometrical problem, which can provide insightful way to understand the dynamic nature of the fuel-balanced reference trajectories planning issue.

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Chien, Y. P., and Qing Xue. "Trajectory planning for coordinately operating robots." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 4, no. 3 (1990): 165–77. http://dx.doi.org/10.1017/s0890060400002365.

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An efficient locally minimum-time trajectory planning algorithm for coordinately operating multiple robots is introduced. The task of the robots is to carry a common rigid object from an initial position to a final position along a given path in three-dimensional workspace in minimum time. The number of robots in the system is arbitrary. In the proposed algorithm, the desired motion of the common object carried by the robots is used as the key to planning of the trajectories of all the non-redundant robots involved. The search method is used in the trajectory planning. The planned robot trajectories satisfy the joint velocity, acceleration and torque constraints as well as the path constraints. The other constraints such as collision-free constraints, can be easily incorporated into the trajectory planning in future research.

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Thoroughman, Kurt A., Wei Wang, and Dimitre N. Tomov. "Influence of Viscous Loads on Motor Planning." Journal of Neurophysiology 98, no. 2 (2007): 870–77. http://dx.doi.org/10.1152/jn.01126.2006.

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Here we computationally investigate how encumbering the hand could alter predictions made by the minimum torque change (MTC) and minimum endpoint variance hypotheses (MEPV) of movement planning. After minutes of training, people have made arm trajectories in a robot-generated viscous force field that were similar to previous baseline trajectories without the force field. We simulate the human arm interacting with this viscous load. We found that the viscous forces clearly differentiated MTC and MEPV predictions from both minimum-jerk predictions and from human behavior. We conclude that learned behavior in the viscous environment could arise from minimizing kinematic costs but could not arise from a minimization of either torque change or endpoint variance.

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Wang, Xin, Nan Li, Jiaming Li, et al. "Optimized Deep Brain Stimulation Surgery to Avoid Vascular Damage: A Single-Center Retrospective Analysis of Path Planning for Various Deep Targets by MRI Image Fusion." Brain Sciences 12, no. 8 (2022): 967. http://dx.doi.org/10.3390/brainsci12080967.

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Co-registration of stereotactic and preoperative magnetic resonance imaging (MRI) images can serve as an alternative for trajectory planning. However, the role of this strategy has not yet been proven by any control studies, and the trajectories of commonly used targets have not been systematically studied. The purpose of this study was to analyze the trajectories for various targets, and to assess the role of trajectories realized on fused images in preventing intracranial hemorrhage (ICH). Data from 1019 patients who underwent electrode placement for deep brain stimulation were acquired. Electrode trajectories were not planned for 396 patients, whereas trajectories were planned for 623 patients. Preoperative various MRI sequences and frame-placed MRI images were fused for trajectory planning. The patients’ clinical characteristics, the stereotactic systems, intracranial hemorrhage cases, and trajectory angles were recorded and analyzed. No statistically significant differences in the proportions of male patients, patients receiving local anesthesia, and diseases or target distributions (p > 0.05) were found between the trajectory planning group and the non-trajectory planning group, but statistically significant differences were observed in the numbers of both patients and leads associated with symptomatic ICH (p < 0.05). Regarding the ring and arc angle values, statistically significant differences were found among various target groups (p < 0.05). The anatomic structures through which leads passed were found to be diverse. Trajectory planning based on MRI fusion is a safe technique for lead placement. The electrode for each given target has its own relatively constant trajectory.

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Rodriguez, Ivan D., Blai Bonet, Sebastian Sardiña, and Hector Geffner. "Flexible FOND Planning with Explicit Fairness Assumptions." Proceedings of the International Conference on Automated Planning and Scheduling 31 (May 17, 2021): 290–98. http://dx.doi.org/10.1609/icaps.v31i1.15973.

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We consider the problem of reaching a propositional goal condition in fully-observable non-deterministic (FOND) planning under a general class of fairness assumptions that are given explicitly. The fairness assumptions are of the form A/B and say that state trajectories that contain infinite occurrences of an action a from A in a state s and finite occurrence of actions from B, must also contain infinite occurrences of action a in s followed by each one of its possible outcomes. The infinite trajectories that violate this condition are deemed as unfair, and the solutions are policies for which all the fair trajectories reach a goal state. We show that strong and strong-cyclic FOND planning, as well as QNP planning, a planning model introduced recently for generalized planning, are all special cases of FOND planning with fairness assumptions of this form which can also be combined. FOND+ planning, as this form of planning is called, combines the syntax of FOND planning with some of the versatility of LTL for expressing fairness constraints. A new planner is implemented by reducing FOND+ planning to answer set programs, and the performance of the planner is evaluated in comparison with FOND and QNP planners, and LTL synthesis tools.

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HARADA, KENSUKE, SHUUJI KAJITA, KENJI KANEKO, and HIROHISA HIRUKAWA. "AN ANALYTICAL METHOD FOR REAL-TIME GAIT PLANNING FOR HUMANOID ROBOTS." International Journal of Humanoid Robotics 03, no. 01 (2006): 1–19. http://dx.doi.org/10.1142/s0219843606000643.

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This paper studies real-time gait planning for a humanoid robot. By simultaneously planning the trajectories of the COG (Center of Gravity) and the ZMP (Zero Moment Point), a fast and smooth change of gait can be realized. The change of gait is also realized by connecting the newly calculated trajectories to the current ones. While we propose two methods for connecting two trajectories, i.e. the real-time method and the quasi-real-time one, we show that a stable change of gait can be realized by using the quasi-real-time method even if the change of the step position is significant. The effectiveness of the proposed methods are confirmed by simulation and experiment.

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Boryga, Marek, Paweł Kołodziej, and Krzysztof Gołacki. "The Use of Asymmetric Polynomial Profiles for Planning a Smooth Trajectory." Applied Sciences 12, no. 23 (2022): 12284. http://dx.doi.org/10.3390/app122312284.

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This paper presents planning of smooth trajectories using the asymmetric profiles of displacement, velocity, acceleration and jerk of described higher degree polynomials. The presented way of determination of polynomial and asymmetry coefficients as well as motion time includes the procedure at both constraints of single kinematic quantities, i.e., velocity, acceleration, jerk and introducing a few constraints simultaneously. Moreover, the paper presents a method of planning trajectories with intermediate points consisting in concatenation of the analyzed polynomials. The proposed method of trajectory planning was compared to that of using the S-curve. The results in the form of kinematic quantity courses are presented graphically. The discussed method guarantees continuity of displacement, velocity, acceleration and jerk. It can be used for planning trajectories of various technical objects (e.g., manipulators, mobile robots, CNC machine tools, optical disk drives, autonomous vehicles, etc.).

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El Ganaoui-Mourlan, Ouafae, Stephane Camp, Thomas Hannagan, Vaibhav Arora, Martin De Neuville, and Vaios Andreas Kousournas. "Path Planning for Autonomous Platoon Formation." Sustainability 13, no. 9 (2021): 4668. http://dx.doi.org/10.3390/su13094668.

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In the context of automated highway systems (AHS), this work proposes an approach that enables a vehicle to autonomously join a platoon with optimized trajectory in the presence of dynamical traffic obstacles. A notable aspect is the use of Model Predictive Control (MPC) optimization of the planned path, in conjunction with a variant of the Rapidly-exploring Random Trees (RRT*) algorithm for the purpose of platoon formation. This combination efficiently explores the space of possible trajectories, returning trajectories that are smoothened out with respect to the dynamic constraints of the vehicle, while at the same time allowing for real-time implementation. The implementation we propose takes into consideration both localization and mapping through relevant sensors and V2V communication. The complete algorithm is tested over various nominal and worst-case scenarios, qualifying the merits of the proposed methodology.

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Chen, Chuanming, Zhen Ye, Fan Hu, Shan Gong, Liping Sun, and Qingying Yu. "Vehicle trajectory-clustering method based on road-network-sensitive features." Journal of Intelligent & Fuzzy Systems 41, no. 1 (2021): 2357–75. http://dx.doi.org/10.3233/jifs-211270.

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Existing trajectory-clustering methods do not consider road-network connectivity, road directionality, and real path length while measuring the similarity between different road-network trajectories. This paper proposes a trajectory-clustering method based on road-network-sensitive features, which can solve the problem of similarity metrics among trajectories in the road network, and effectively combine their local and overall similarity features. First, the method performs the primary clustering of trajectories based on the overall vehicle motion trends. Then, the map-matched trajectories are clustered based on the road segment density, connectivity, and corner characteristics. Finally, clustering is then merged based on the multi-area similarity measure. The visualization and experimental results on real road-network trajectories show that the proposed method is more effective and comprehensive than existing methods, and more suitable for urban road planning, public transportation planning, and congested road detection.

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Yamamoto, M., H. Ozaki, and A. Mohri. "Planning of manipulator joint trajectories by an iterative method." Robotica 6, no. 2 (1988): 101–5. http://dx.doi.org/10.1017/s0263574700003908.

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SUMMARYManipulator joint trajectories are planned to make an arbitrary cost function as good as possible in consideration of physical constraints based on kinematics and dynamics of a manipulator system. An algorithm presented in this paper is an iteratively improving method using the local controllability of B spline. It can be also applied to the case that some points are specified and joint trajectories must pass through those points. This algorithm is applied to an example of trajectory planning of a manipulator with two links and two degrees of freedom.

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Wang, Xuyang, Tiansheng Lu, and Peiyan Zhang. "Study on State Transition Method Applied to Motion Planning for a Humanoid Robot." International Journal of Advanced Robotic Systems 4, no. 3 (2007): 37. http://dx.doi.org/10.5772/5683.

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This paper presents an approach of motion planning for a humanoid robot using a state transition method. In this method, motion planning is simplified by introducing a state-space to describe the whole motion series. And each state in the state-space corresponds to a contact state specified during the motion. The continuous motion is represented by a sequence of discrete states. The concept of the transition between two neighboring states, that is the state transition, can be realized by using some traditional path planning methods. Considering the dynamical stability of the robot, a state transition method based on search strategy is proposed. Different sets of trajectories are generated by using a variable 5th-order polynomial interpolation method. After quantifying the stabilities of these trajectories, the trajectories with the largest stability margin are selected as the final state transition trajectories. Rising motion process is exemplified to validate the method and the simulation results show the proposed method to be feasible and effective.

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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 (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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Yu, Jiaming, Hao Sun, Qinglin Sun, Mingwei Sun, and Zengqiang Chen. "A High-Feasibility Real-Time Trajectory-Planning Method for Parafoils Based on a Flexible Dynamic Model." Mathematics 12, no. 24 (2024): 3913. https://doi.org/10.3390/math12243913.

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Effective trajectory planning is critical for achieving precise autonomous navigation and safe landing of parafoil delivery systems. However, current parafoil trajectory planning still faces challenges in ensuring consistency between actual system behavior and algorithmic real-time performance. Due to the strong fluid–structure interaction (FSI) between the flexible canopy and airflow, traditional dynamic models based on point mass and rigid-body assumptions often lack aerodynamic accuracy. These models produce planned trajectories in simulation environments that are inconsistent with the actual system’s behavior and cannot directly provide an effective reference for airdrop experiments. Additionally, traditional planning methods require a significant amount of time to calculate complex dynamic models and generate fixed trajectories in advance. These methods not only fail to provide usable results in a short period of time, but also cannot prevent the accumulation of tracking errors by adjusting the target trajectory in real time. To address these issues, this paper proposes a flexible 8-degree-of-freedom (8-DOF) dynamic model based on the FSI method, utilizing the actual aerodynamic parameters of the canopy to achieve improved consistency with the behavior of the actual system. The Soft Actor–Critic (SAC) algorithm is then employed to achieve real-time trajectory planning for parafoil airdrop systems, addressing the real-time planning performance limitations of traditional algorithms. The airdrop experiments validate that the simulation trajectories generated using this model demonstrate higher consistency with actual flight trajectories, providing more accurate references for pre-flight trajectory optimization. Moreover, the proposed method enables real-time trajectory planning and dynamically adjusts target trajectories based on the current position and attitude of the parafoil, effectively mitigating the accumulation of errors.

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Journal articles on the topic 'Planning of trajectories'

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