A numerical technique for planning motion strategies of a mobile robot in presence of uncertainty

Abstract

This paper addresses the problem of planning the motions of a circular mobile robot moving amidst polygonal obstacles with uncertainty i n robot control and sensing. T h e robot is equipped with sensors which, if properly used, m a y provide information t o overcome the uncertainty accumulated during the motions. T h e position sensor is based o n dead-reckoning, the error t h e n results i n t o a cumulative uncertainty. A proximity sensor m a y be used t o localize the robot with respect to the obstacles of the environment. T h e robot can also gain information by entering inside landmark areas where the position error is assumed to be bounded. W e describe a planner which produces robust motion strategies composed of sensor-based m o t i o n comm a n d s which guarantee that, given a n explicit model of the error accumulated b y t h e m o t i o n commands, the robot canreach safely its goal with a n error lower than a pre-specified value. It is based o n a propagation of a numericalpotential and o n a geometric unalysis of the reachability of environmental features. T h i s planner exhibits a set of powerful Capabilities: while it allows t o consider motion primitives which accumulate uncertainty, it is able, whenever possible, t o navigate without relocalizing the robot when the task does n o t impose it, and also to m a k e a proper use of the sensors. Several examples r u n with the planner are presented a t the end of the paper.

LQG-MP: Optimized Path Planning for Robots with Motion Uncertainty and Imperfect State Information

“…The sensing uncertainty is taken into account in the planner of [31], which aims to optimize the information content along a path. Planners in [5,7,21] assume that landmark regions exist in the environment where the accumulated motion uncertainty can be "reset".…”

A Bayesian framework for optimal motion planning with uncertainty

“…This paper is concerned with two problems: minimizing the execution time, or minimizing the final covariance (with a bound on the execution time). Some approaches (e.g., [4], [5]) tried to solve a simpler problem: finding an admissible plan, without optimality properties. Other works ( [6]) try to maximize the collected information, with free final pose.…”

“…There are two main options for representing uncertainty: a probabilistic representation, in terms of covariances, or a set-membership approach. In the set-membership approach ( [5], [4]), the uncertainty is represented by a poseq(t) and a set SU(t). The assumption is that the true pose q(t) belongs to the set obtained by enlargingq(t) by the set SU(t): q(t) ∈q(t) ⊕ SU(t) (here ⊕ denotes morphological dilatation).…”

“…In some other cases ( [1]), the plan is a reference trajectory, along which the motion is guaranteed to be safe, in spite of uncertainty -this is also our case. Finally, the output of some methods ( [13], [4]) is a 'sensorbased motion': a sequence of action/termination condition, where the condition depends on the sensory input ("walk until you see the wall").…”

“…In chronological order, the main family of approaches in the literature have been pre-image back-chaining [17], [13], [18]; sensory uncertainty fields [8], [19], [20], [21]; sensorbased planning [22], [4], [23]; the Information Space approach [10]; the set-membership approach [24], [5]; stochastic dynamic programming [15], [25]; and classical search strategies in an extended space [12], [1], [9], [26], [27]. The latter is the family to which this paper belongs.…”