MM-LMPC: Multi-Modal Learning Model Predictive Control via Mode-Specific Terminal Design and Bandit-Based Exploration

Abstract

Learning Model Predictive Control (LMPC) improves iterative control tasks by using previous executions to construct the terminal constraint and terminal cost of the MPC problem. Although effective, this reuse of past trajectories can make LMPC sensitive to the initial data. In particular, LMPC may repeatedly exploit stored trajectories with favorable cost-to-go values while insufficiently exploring alternative route patterns that could yield lower cost after further improvement. To address this issue, we propose Multi-Modal LMPC (MM-LMPC). The proposed framework clusters past trajectories into motion modes, constructs a mode-specific LMPC controller for each mode, and uses an LCB-based meta-controller to select which mode-specific controller to execute at each iteration. Mode information is incorporated into the terminal constraint and terminal cost through two designs. The hard-constrained design uses mode-specific terminal constraints and terminal costs constructed from the data associated with each mode. The soft-regularized design retains a shared terminal constraint while adding membership-based penalties to the terminal cost. These designs reduce the bias caused by pooling all trajectories into a single terminal memory while retaining the recursive feasibility and stability structure of LMPC. Our theoretical analysis shows that both designs preserve recursive feasibility and closed-loop stability. For the hard-constrained design, we further establish mode-wise cost convergence, asymptotic best-mode performance, and a logarithmic cumulative regret bound under the LCB rule. Simulations on multi-route obstacle-avoidance tasks show that MM-LMPC improves exploration and achieves lower costs than standard LMPC.