Vehicle Motion Planning with Time-Varying Constraints

Introduction With the growing emphasis on vehicle autonomy, the problem of planning a trajectory in an environment with obstacles has become increasingly important. This task has been of particular interest to roboticists and computer scientists, whose primary focus is on kinematic motion planning [1]. Typical kinematic planning methods fall into two main categories, roadmap methods and incremental search methods, both of which find collision-free paths in the state space. Roadmap methods generate and traverse a graph of collision-free connecting paths spanning the state space, while incremental search methods, including dynamic programming [2] and potential field methods [3], perform an iterative search to connect the initial and goal states. For the purely geometric path planning problem, deterministic algorithms have been created that are complete, i.e., they will find a solution if and only if one exists. Unfortunately, these suffer from high computational costs which are exponential in system degrees of freedom. This cost has motivated the development of iterative randomized path planning algorithms that are probabilistically complete, i.e., if a feasible path exists, the probability of finding a path from the initial to final conditions converges to one as the number of iterations goes to infinity. The introduction of the Rapidly-exploring Random Trees (RRTs) of LaValle and Kuffner [4] allowed both for computationally efficient exploration of a complicated space as well as incorporation of system dynamics. The RRT grows a tree of feasible trajectories from the initial condition, or root node. Each node, or waypoint, on the tree represents a system state and has possible trajectories branching from it. Through use of an embedded planning routine, the tree incrementally builds itself in random direcSenior Member of Technical Staff, currently at The Aerospace Corporation, 15049 Conference Center Drive, Suite 1029, Chantilly, VA 20151, Member AIAA Assistant Professor, Coordinated Sciences Laboratory, 1308 West Main Street, Urbana, IL 61801 Associate Professor, Department of Aerospace Engineering, 104 South Wright Street, Urbana, IL 61801, Associate Fellow AIAA