Efficient Computation of Inner Approximations of Reachable Sets for a Verified Motion Planning Concept

Verification of control systems often involves the computation of reachable sets. In this context, reachable sets are used to verify that a system is capable of reaching a desired set of states or that it will not reach a set of undesired states. This contribution presents a novel method for computing convex inner approximations of reachable sets for non-linear input-affine systems with constrained inputs. The inner approximation is obtained using the reachable set of the linearized system that is shrunk by a factor depending on the linearization errors. The proposed method is integrated into a motion planning concept for mobile robots. In this way, the motion planning concept guarantees, that motions that are planned based on a simplified model of a robot can be reached by an accurate model of the robot. The application example demonstrates the computational efficiency of the proposed method as it is utilized to compute inner approximated reachable sets of a system that consists of 18 states and features eight inputs.