BP-RRT: Barrier Pair Synthesis for Temporal Logic Motion Planning

TL;DR

This paper introduces BP-RRT, an algorithm combining barrier pairs and rapidly-exploring random trees to synthesize controllers for nonlinear systems under linear temporal logic constraints, demonstrated on a robot simulation.

Contribution

The paper presents a novel algorithm that integrates barrier pairs with RRT to efficiently solve non-convex control synthesis problems for temporal logic specifications.

Findings

Successfully synthesized controllers for a two-link robot manipulator.

Effectively handled non-convex constraints in control synthesis.

Demonstrated the approach's viability through simulation results.

Abstract

For a nonlinear system (e.g. a robot) with its continuous state space trajectories constrained by a linear temporal logic specification, the synthesis of a low-level controller for mission execution often results in a non-convex optimization problem. We devise a new algorithm to solve this type of non-convex problems by formulating a rapidly-exploring random tree of barrier pairs, with each barrier pair composed of a quadratic barrier function and a full state feedback controller. The proposed method employs a rapid-exploring random tree to deal with the non-convex constraints and uses barrier pairs to fulfill the local convex constraints. As such, the method solves control problems fulfilling the required transitions of an automaton in order to satisfy given linear temporal logic constraints. At the same time it synthesizes locally optimal controllers in order to transition between the regions corresponding to the alphabet of the automaton. We demonstrate this new algorithm on a simulation of a two linkage manipulator robot.