MP-MPPI: A Motion Primitive Guided Sampling-Based Optimizer for Model Predictive Control

Sampling-based model predictive control methods like MPPI and CEM are essential for real-time control of nonlinear robotic systems, particularly where discontinuous dynamics preclude gradient-based optimization. However, these methods derive from information-theoretic objectives that are agnostic to the geometry of the control problem, leading to pathological behaviors such as mode-averaging when the cost landscape is complex. We present OT-MPC, a sampling-based algorithm that overcomes these limitations through an entropy-regularized optimal transport formulation. By computing an optimal coupling between candidate control sequences and low-cost proposals, OT-MPC refines candidates toward nearby promising samples while coordinating updates across the ensemble to maintain coverage of the solution space. We derive closed-form, gradient-free updates via the Sinkhorn algorithm, enabling real-time performance. Experiments on navigation, manipulation, and locomotion tasks demonstrate improved success rates over existing methods.

This paper presents an efficient model predictive path integral (MPPI) control framework for systems with complex nonlinear dynamics. To improve the computational efficiency of classic MPPI while preserving control performance, we replace the nonlinear dynamics used for trajectory propagation with a learned linear deep Koopman operator (DKO) model, enabling faster rollout and more efficient trajectory sampling. The DKO dynamics are learned directly from interaction data, eliminating the need for analytical system models. The resulting controller, termed MPPI-DK, is evaluated in simulation on pendulum balancing and surface vehicle navigation tasks, and validated on hardware through reference-tracking experiments on a quadruped robot. Experimental results demonstrate that MPPI-DK achieves control performance close to MPPI with true dynamics while substantially reducing computational cost, enabling efficient real-time control on robotic platforms.

Classical proportional--integral--derivative (PID) control remains widely used in industrial control systems, while model predictive control (MPC) is actively studied to achieve higher performance for systems with nonlinear dynamics. Model predictive path integral (MPPI) control is a sampling-based MPC method that optimizes control inputs without gradient calculations and can handle non-differentiable models and objective functions. However, conventional MPPI directly samples control-input sequences, which can produce large temporal input increments and causes the optimization dimension to grow with the prediction horizon. This study proposes MPPI--PID control, which uses MPPI to optimize PID gains online instead of directly optimizing the control-input sequences. By replacing high-dimensional input-sequence optimization with low-dimensional gain-space optimization while retaining the PID structure, the proposed formulation improves sampling efficiency and promotes smoother control inputs. Theoretical analyses are provided for a unified path-integral update, the relation between optimization dimension and effective sample size, and the temporal correlation of input perturbations induced by the PID structure. The method is evaluated on a learning-based path following of a mini forklift using a residual-learning dynamics model that combines a physical model and a neural network identified from real-machine driving data. Numerical results show that MPPI--PID improves tracking performance over fixed-gain PID, yields smaller input increments than conventional MPPI, and maintains favorable performance under reduced sampling budgets.