Markus Walker

Markus Walker, Daniel Frisch, Uwe D. Hanebeck

Cross-entropy method model predictive control (CEM--MPC) is a powerful gradient-free technique for nonlinear optimal control, but its performance is often limited by the reliance on random sampling. This conventional approach can lead to inefficient exploration of the solution space and non-smooth control inputs, requiring a large number of samples to achieve satisfactory results. To address these limitations, we propose deterministic sampling CEM (dsCEM), a novel framework that replaces the random sampling step with deterministic samples derived from localized cumulative distributions (LCDs). Our approach introduces modular schemes to generate and adapt these sample sets, incorporating temporal correlations to ensure smooth control trajectories. This method can be used as a drop-in replacement for the sampling step in existing CEM-based controllers. Experimental evaluations on two nonlinear control tasks demonstrate that dsCEM consistently outperforms state-of-the-art iCEM in terms of cumulative cost and control input smoothness, particularly in the critical low-sample regime.

Markus Walker, Marcel Reith-Braun, Tai Hoang et al.

Sampling-based model predictive control (MPC) is effective for nonlinear systems but often produces non-smooth control inputs due to random sampling. To address this issue, we extend the model predictive path integral (MPPI) framework with deterministic sampling and improvements from cross-entropy method (CEM)--MPC, such as iterative optimization, proposing deterministic sampling MPPI (dsMPPI). This combination leverages the exponential weighting of MPPI alongside the efficiency of deterministic samples. Experiments demonstrate that dsMPPI achieves smoother trajectories compared to state-of-the-art methods.

Markus Walker, Marcel Reith-Braun, Daniel Frisch et al.

Sampling-based model predictive control (MPC) algorithms, such as model predictive path integral (MPPI), enable approximate, gradient-free solutions to optimal control problems by drawing samples from a proposal distribution, evaluating their trajectory costs, and updating the proposal parameters accordingly. However, these approaches typically rely on heuristics for adjusting hyperparameters, such as temperature or momentum, or manual tuning. We propose a trust region formulation for sampling-based MPC that constrains updates of the proposal distribution via a principled Kullback--Leibler (KL) divergence bound and, optionally, an entropy lower bound. This replaces heuristic hyperparameter adaptation with values that are optimal w.r.t. the underlying Lagrangian. We further improve sample efficiency and convergence by combining the trust region update with deterministic localized cumulative distribution (LCD)-based sampling. Experiments on two benchmark environments demonstrate that the proposed trust region update achieves faster convergence and better sample efficiency in low-sample and low-iteration regimes, especially when paired with deterministic LCD-based sampling.