Convex Approximation for LTL-based Planning

Abstract

We present a formulation for linear temporal logic (LTL)-based task planning of nonlinear dynamical systems. We consider pick-and-place task planning as a typical example of the planning task that can be modeled as a hybrid system that includes the states of robots and objects. LTL-based planning for hybrid systems is solved as a mixed-integer problem (MIP), especially a mixed-integer linear programming problem (MILP). Due to the formulation by the MILP, we could only deal with linear systems and linear constraints. In our proposed method, we apply a convex approximation to systems that have bilinear terms and quadratic terms in their dynamics. And we incorporate nonlinear systems into existing LTL-based planning as an MILP. We demonstrate the effectiveness through numerical simulations of a simple robot arm system and drone system.