Robot Motion Planning: A Game-Theoretic Foundation

Abstract

Analysis techniques and algorithms for basic path planning have become quite valuable in a variety of applications such as robotics, virtual prototyping, computer graphics, and computational biology. Yet, basic path planning represents a very restricted version of general motion planning problems often encountered in robotics. Many problems can involve complications such as sensing and model uncertainties, nonholonomy, dynamics, multiple robots and goals, optimality criteria, unpredictability, and nonstationarity, in addition to standard geometric workspace constraints. This paper proposes a unified, game-theoretic mathematical foundation upon which analysis and algorithms can be developed for this broader class of problems, and is inspired by the similar benefits that were obtained by using unified configuration-space concepts for basic path planning. By taking this approach, a general algorithm has been obtained for computing approximate optimal solutions to a broad class of motion planning problems, including those involving uncertainty in sensing and control, environment uncertainties, and the coordination of multiple robots.

An experimental study of distributed robot coordination

“…This rules out certain trivial coordination schemas, like for example the one where just one robot moves and all the others remain stationary, since the overall time would be too high. LaValle and Hutchinson solved the problem using a game-theoretic approach based on multi-objective optimization [9][10]. The approach allows to tune the algorithm behavior between centralized planning and complete decentralized planning.…”

Convex Hull Asymptotic Shape Evolution

“…The experimental successes of RRTs have stimulated interest in their theoretical properties. In [10], it was established that the vertex distribution converges in probability to the sampling distribution. It was also noted that there is a "Voronoi bias" in the tree growth because the probability that a vertex is selected is proportional to the volume of its Voronoi region.…”

Motion Planning Under Uncertainty: Application to an Unmanned Helicopter

“…The uncertainty in the environment is treated as a deterministic worst case 14,15 or on a probabilistic average case basis. 16 In "probabilistic robotics", there has been substantial research in the localization of a mobile robot while simultaneously mapping the environment. 17, , , , 18 19 20 21 In recent years, there has been a blending of previously different areas of study: planning, control theory, and artificial intelligence for motion planning.…”