Bounds on tracking error using closed-loop rapidly-exploring random trees

• Main Authors: Luders, Brandon Douglas (Contributor), Karaman, Sertac (Contributor), Frazzoli, Emilio (Contributor), How, Jonathan P. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Aeronautics and Astronautics (Contributor), Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers, 2010-10-06T14:42:45Z.
• Subjects: Article
• Online Access: Get fulltext

This paper considers the real-time motion planning problem for autonomous systems subject to complex dynamics, constraints, and uncertainty. Rapidly-exploring random trees (RRT) can be used to efficiently construct trees of dynamically feasible trajectories; however, to ensure feasibility, it is critical that the system actually track its predicted trajectory. This paper shows that under certain assumptions, the recently proposed closed-loop RRT (CL-RRT) algorithm can be used to accurately track a trajectory with known error bounds and robust feasibility guarantees, without the need for replanning. Unlike open-loop approaches, bounds can be designed on the maximum prediction error for a known uncertainty distribution. Using the property that a stabilized linear system subject to bounded process noise has BIBO-stable error dynamics, this paper shows how to modify the problem constraints to ensure long-term feasibility under uncertainty. Simulation results are provided to demonstrate the effectiveness of the closed-loop RRT approach compared to open-loop alternatives.
United States. Air Force Office of Scientific Research (grant FA9550-08-1-0086)