Randomized searches and nonlinear programming in trajectory planning

This paper presents a novel trajectory planning algorithm for nonlinear dynamical systems evolving in environments with complex obstacles. The incremental search algorithm entails: (1) a global exploration strategy based on randomization and on a rapidly-exploring heuristic; and (2) a local planner based on collocation and nonlinear programming. To numerically validate the design, we consider a six degree of freedom vehicle model subject to saturation limits on the control inputs and obstacles on the state variables. Experimental results indicate that the proposed scheme outperforms implementations based solely on nonlinear programming or on randomization.

[1]  R. A. Mayo.  Relative Quaternion State Transition Relation , 1979 .

[2]  Bruce A. Conway,et al.  Discrete approximations to optimal trajectories using direct transcription and nonlinear programming , 1992 .

[3]  Jean-Claude Latombe,et al.  Robot Motion Planning: A Distributed Representation Approach , 1991, Int. J. Robotics Res..

[4]  Oskar von Stryk,et al.  Direct and indirect methods for trajectory optimization , 1992, Ann. Oper. Res..

[5]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[6]  Dinesh Manocha,et al.  Fast contact determination in dynamic environments , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[7]  Lydia E. Kavraki,et al.  Probabilistic roadmaps for path planning in high-dimensional configuration spaces , 1996, IEEE Trans. Robotics Autom..

[8]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[9]  J. Betts.  Survey of Numerical Methods for Trajectory Optimization , 1998 .

[10]  Dinesh Manocha,et al.  Fast Proximity Queries with Swept Sphere Volumes , 1999 .

[11]  Emilio Frazzoli,et al.  A hybrid control architecture for aggressive maneuvering of autonomous helicopters , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[12]  Jean-Claude Latombe,et al.  Motion Planning: A Journey of Robots, Molecules, Digital Actors, and Other Artifacts , 1999, Int. J. Robotics Res..

[13]  F. Bullo,et al.  Motion planning for nonlinear underactuated vehicles using H/sup /spl infin// techniques , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[14]  S. LaValle,et al.  Randomized Kinodynamic Planning , 2001 .