Toward efficient trajectory planning: the path-velocity decomposition
International Journal of Robotics Research
Planning of minimum-time trajectories for robot arms
International Journal of Robotics Research
Collision-free motion planning of two robots
IEEE Transactions on Systems, Man and Cybernetics
Integer and combinatorial optimization
Integer and combinatorial optimization
Real-time pathfinding in multirobot systems including obstacle avoidance
International Journal of Robotics Research
An exact algorithm for kinodynamic planning in the plane
Discrete & Computational Geometry
Journal of the ACM (JACM)
Motion planning in the presence of moving obstacles
Journal of the ACM (JACM)
Practical methods for optimal control using nonlinear programming
Practical methods for optimal control using nonlinear programming
Robot Motion Planning and Control
Robot Motion Planning and Control
Robot Motion Planning
Safe Cooperative Robot Dynamics on Graphs
SIAM Journal on Control and Optimization
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
From Paths to Trajectories for Multi-body Mobile Robots
Proceedings of the 5th International Symposium on Experimental Robotics V
On optimal cooperative conflict resolution for air traffic management systems
IEEE Transactions on Intelligent Transportation Systems
IEEE Transactions on Intelligent Transportation Systems
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
An experimental study of distributed robot coordination
Robotics and Autonomous Systems
Multi-robot coordination using generalized social potential fields
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Multi-vehicle path coordination in support of communication
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Generalized velocity obstacles
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
A two-stage ILP-based droplet routing algorithm for pin-constrained digital microfluidic biochips
Proceedings of the 19th international symposium on Physical design
Modeling collision avoidance behavior for virtual humans
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 2 - Volume 2
Path planning for groups using column generation
MIG'10 Proceedings of the Third international conference on Motion in games
Optimal Testing of Digital Microfluidic Biochips
INFORMS Journal on Computing
Safe distributed motion coordination for second-order systems with different planning cycles
International Journal of Robotics Research
Collision free cooperative navigation of multiple wheeled robots in unknown cluttered environments
Robotics and Autonomous Systems
Journal of Intelligent and Robotic Systems
Offline gain optimization in kinodynamic motion planning based on a harmonic potential field
Artificial Life and Robotics
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This paper focuses on the collision-free coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical programming, consists of identifying collision segments along each robot's path, and then optimizing the robots' velocities along the collision and collision-free segments. First, for each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding two-point boundary value problems. The collision avoidance constraints for pairs of robots can then be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations, which provide schedules that give lower and upper bounds on the optimum; the upper bound schedule is designed to provide continuous velocity trajectories that are feasible. The approach is illustrated with coordination of multiple robots, modeled as double integrators subject to velocity and acceleration constraints. An application to coordination of nonholonomic car-like robots is described, along with implementation results for 12 robots.