A path-space search algorithm for motion planning with uncertainties

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).…”

“…As for the exteroceptive sensors, one can choose to model the fact that a sensor is a source of continuous information, and the robot collects new information also by just standing still; this is the model used in this paper. Or, one could model an exteroceptive sensor as a device that allows a bounded uncertainty in its working zone, but this uncertainty does not decrease with time ( [5]). Another sensing option is the use of "safe areas" (e.g., [13]).…”

“…The methods reviewed here have solved the problem in a variety of ways, covering most, if not all, known planning methods: back-projection [13], value/policy iteration [10], gradient descent [5], analytic closed-form solution [6], multi-sine optimization [14], classical graph search [1], dynamic programming [15], RRT [2], POMDPs [16].…”

“…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.…”