BP-RRT: Barrier Pair Synthesis for Temporal Logic Motion Planning
This addresses motion planning for robots with temporal logic specifications, but it appears incremental as it builds on existing RRT and barrier pair methods.
The paper tackles the non-convex optimization problem in synthesizing low-level controllers for robots under linear temporal logic constraints by proposing BP-RRT, an algorithm that uses a rapidly-exploring random tree of barrier pairs to handle non-convex constraints and fulfill local convex constraints, demonstrated on a two-link manipulator simulation.
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.