Robust MPC-based Abstraction for Motion Planning of a Mobile Robot

This paper addresses the problem of motion planning for a constrained mobile robot. One of the challenges in this field is the complexity of the planning scenarios, which could no longer be formulated with common problems in control theory such as stability and regulation. In this regard, Linear Temporal Logic (LTL) formulas from computer science theories can be used to express high-level motion planning missions. Therefore, it covers a wide variety of planning scenarios such as surveillance, recurrence, sequencing tasks, etc. Here, we proposed a novel robust MPC-based abstraction to abstract the dynamical behavior of a controlled mobile robot in the environment. As a result, the finite state model of the robot is obtained and modeled with Weighted Transition System (WTS). In parallel, the desired objectives defined by LTL are transferred to the corresponding Buchi Automata (BA) in the cyber domain. This makes it straightforward to carry out further computations in the cyber domain by exploiting the rich ideas of model checking from formal methods. At last, the generated plan is modified by the modulated matrix to avoid possible obstacles and then refined into a Hybrid Automata (HA) in a closed-loop to implement the desired specifications. Illustrative simulations are presented to evaluate the applicability of the proposed approach.