Iterative Model Predictive Control for Piecewise Systems

TL;DR

This paper introduces an iterative MPC approach for piecewise nonlinear systems, ensuring safety and goal achievement through policy iteration, demonstrated on a SLIP model with robustness to disturbances.

Contribution

The paper proposes a novel iterative MPC method for piecewise systems that guarantees safety and finite-time convergence, with demonstrated robustness and effectiveness on a complex model.

Findings

Successfully steers system to goal state within finite time.

Method is robust to initial condition variations and disturbances.

Effective in minimum time control tasks.

Abstract

In this paper, we present an iterative Model Predictive Control (MPC) design for piecewise nonlinear systems. We consider finite time control tasks where the goal of the controller is to steer the system from a starting configuration to a goal state while minimizing a cost function. First, we present an algorithm that leverages a feasible trajectory that completes the task to construct a control policy which guarantees that state and input constraints are recursively satisfied and that the closed-loop system reaches the goal state in finite time. Utilizing this construction, we present a policy iteration scheme that iteratively generates safe trajectories which have non-decreasing performance. Finally, we test the proposed strategy on a discretized Spring Loaded Inverted Pendulum (SLIP) model with massless legs. We show that our methodology is robust to changes in initial conditions and disturbances acting on the system. Furthermore, we demonstrate the effectiveness of our policy iteration algorithm in a minimum time control task.