Navigation in a multi-obstacle environment. From partition of the space to a zonotopic-based MPC

This paper pertains to the navigation in a multi-obstacle environment and advocates the use of local zonotopic approximations. The design problem is commonly stated in the literature in terms of a constrained optimization problem over a non-convex domain. We show that a partition of the navigation space can be obtained using convex liftings, providing the means to generate a path from the current to a final position. The feasible domain is efficiently described using zonotopes which have a complexity advantage w.r.t. generic polyhedral sets. This work treats the zonotopic approximations from a control perspective, providing a set of conditions able to safeguard the initial domain topology. An adaptation of the generic collision avoidance problem is considered, aiming to guarantee the feasibility and highlighting through simulations the advantages offered by the zonotopic representation.