PNC-CL a Toolbox for Piecewise Affine Convex-Liftings with Application in Planning and Control Design

The paper describes a novel, publicly available toolbox for piecewise-affine (PWA) convex-lifting. The main goal is to provide a tool for efficient partitions of sets in finite-dimensional spaces with applications in navigation and control design. This objective is achieved by employing a lift-and-project philosophy that relies on performant linear programming optimization and polyhedra manipulation. Once a PWA lifting is constructed, the related polyhedral partition provides an interconnection graph that can be used for path planning, which is considered here as the main application. The paper provides the main theoretical elements of the technique's foundation and describes the toolbox's structure along with the numerical artifacts used for its implementation. Illustrative examples for the practical problems are provided, supporting the claims of efficiency and versatility.