Navigation in a multi-obstacle environment. from partition of the space to a zonotopic-based MPC
Résumé
This paper pertains to the navigation in a multi-obstacle environment and advocates the use of local zonotopic approximations within the obstacle and collision avoidance problem. The design problem is commonly stated in the literature in terms of a constrained optimization problem over a non-convex domain. Firstly, it will be shown that a partition of the navigation space can be obtained using the notion of convex liftings. This partition will offer the foundation for the generation of a path from the current position to the destination point. In order to efficiently describe the navigation on this path, the feasible domain is described using zonotopes. The structural properties of zonotopes with respect to the generic polyhedral sets represents an advantage from the computational point of view. The current paper treats the zonotopic approximations from a control perspective, providing a set of conditions able to safeguard the initial domain topology. Globally, an adaptation of the generic collision avoidance problem is considered, aiming to guarantee the feasibility and highlighting through simulations and proof of concepts illustrations the advantages offered by the use of a zonotopic representation.
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