Time-aware MPC improves control by optimizing switching moments
Switch-Time-Aware Hybrid Model Predictive Control Using the Hybrid Minimum Principle
Robotics
Summary
Controlling systems that switch between different behaviors can be tricky, especially when the timing of these switches matters. The authors present a new way to control such hybrid systems by including the exact times switches happen as part of the solution. This approach solves a smooth optimization problem that finds the best control actions and switch times at once. When tested on a bouncing ball scenario, it achieved better control with less effort and faster calculations compared to older methods.
What this means in practice
- •For robotics engineers: Implement control algorithms that optimize both control inputs and event timings in robots with hybrid dynamics for smoother and more efficient behavior.
- •For automotive control teams: Improve vehicle control systems by jointly optimizing continuous actions and switching times to reduce control effort and improve responsiveness.
Authors
Valentin Gaucher, Wenlong Zhang
Abstract
This article presents a time-aware hybrid model predictive control (MPC) framework that simultaneously optimizes the objective with respect to both continuous control inputs and event switching times. Rather than relying on a fixed time grid, the switching instant is lifted into the decision vector and treated as an explicit optimization variable. The resulting transcription is a smooth nonlinear program whose Karush-Kuhn-Tucker (KKT) conditions are consistent with the Hybrid Minimum Principle (HMP) event-time stationarity condition, so first-order hybrid sensitivities are recovered implicitly through the KKT system rather than by evaluating saltation matrices. Each MPC step solves a single sparse Quadratic Program (QP), jointly optimizing control inputs and impact timing in real time. On a bouncing mass landing on an oscillating platform, the method attaches in half the time of fixed-grid saltation MPC, reduces cumulative control effort by 30%, and removes the post-impact rebounds, at a 15% increase in per-cycle solve time. It matches the cumulative effort of offline time-aware solvers to within 4% while running at 2.4 ms per cycle against 281 ms for a complementarity-based formulation of the same problem, of which a 10.6x reduction is attributable to the transcription alone at a fixed solver.