Optimal Trajectory Planning of Hybrid Systems by Efficient MIQP Encoding

This paper proposes an efficient encoding for Mixed Integer Quadratic Programming (MIQP) problems in optimally controlling constrained hybrid systems from an initial state into a target region over a finite time horizon. The set of admissible trajectories given the system semantics is formulated by tailored constraints involving binary variables to encode the transition dynamics. A subset of these constraints establish a phase sequencing, which reduces the number of possible value combinations for the binary variables significantly, resulting in lower computation times for solving the MIQP problem. An illustrating example demonstrates the low computation times.