Robust Path Planning and Control For Polygonal Environments via Linear Programming

Robust Sample-Based Output-Feedback Path Planning

“…In our algorithm, we use the min-max robust Linear Programming (LP) controller synthesis method from [14]. However, that work assumes that a polyhedral convex cell decomposition of the environment is available, which greatly reduces the applicability of that method.…”

“…We then propose a way to define convex cells around each node in the tree that ensure progress from that node to its parent via a CLF constraint, while using the samples found in collision to form a local convex approximation of the free space for obstacle avoidance via CBF constraints. We apply the method of [14] to formulate a min-max robust Linear Program that synthesizes a controller for each cell which takes as inputs relative position measurements of the landmarks and outputs a control signal that respects and balances the stability constraint from the CLF, and the safety (collision avoidance) constraints from the CBF. Additionally, we show how to easily recompute the controllers (online) to handle the case where subsets of landmarks are not visible (e.g., due to the the camera's limited field of view).…”

“…• Integrate high-level RRT * path planning, with low-level CLF-CBF LP control synthesis, thus allowing the method of [14] to be applied to general environments for which a cell decomposition is not available; • Introduce a new algorithm to simplify and improve a tree generated by RRT * algorithm with a finite number of samples (which, in general, is not optimal). • Introduce a new method to reformulate the controller to navigate with a limited field of view.…”

“…In this work, we assume that Lie derivatives of h(x) of the first order are sufficient [15] (i.e., h(x) has relative degree 1 with respect to the dynamics (1)); however, the result could be extended to the higher relative degree, as discussed in [14].…”

“…Note that, to define a controller for edge (i, j), the landmarks do not necessarily need to belong to X ij , and, in general, each cell could use a different set of landmarks (we explore this direction further in Section III-F). Following the approach of [14], and using the CLF-CBF constraints reviewed in Section II, we encode our goal in the following feasibility problem: find K ij subject to :…”