Reference-Free Sampling-Based Model Predictive Control

TL;DR

The paper addresses the problem of enabling emergent locomotion without gait references or offline pre-training. It proposes a reference-free MPPI framework with a dual-space Hermite spline parameterization and diffusion-inspired noise annealing to explore joint-position and velocity trajectories on CPU hardware. A best-trajectory tracking mechanism and real-time state prediction with warm-starting address robustness under computation delays. Experiments validate emergent gaits, jumping, and balancing on the Go2 quadruped and in simulation on a humanoid, achieving real-time performance with as few as $30$ samples per step and demonstrating cross-platform generality.

Abstract

We present a sampling-based model predictive control (MPC) framework that enables emergent locomotion without relying on handcrafted gait patterns or predefined contact sequences. Our method discovers diverse motion patterns, ranging from trotting to galloping, robust standing policies, jumping, and handstand balancing, purely through the optimization of high-level objectives. Building on model predictive path integral (MPPI), we propose a dual-space spline parameterization that operates on position and velocity control points. Our approach enables contact-making and contact-breaking strategies that adapt automatically to task requirements, requiring only a limited number of sampled trajectories. This sample efficiency allows us to achieve real-time control on standard CPU hardware, eliminating the need for GPU acceleration typically required by other state-of-the-art MPPI methods. We validate our approach on the Go2 quadrupedal robot, demonstrating various emergent gaits and basic jumping capabilities. In simulation, we further showcase more complex behaviors, such as backflips, dynamic handstand balancing and locomotion on a Humanoid, all without requiring reference tracking or offline pre-training.

Figures (4)

• Figure 1: Overview of the reference-free sampling-based MPC framework (top): our approach enables emergent jumping motion experimentally achieved on the Go2 robot without any guiding reference (bottom).
• Figure 2: Sequence illustrating the discovered walking gait on the Go2 quadruped.
• Figure 3: Plot comparison of different spline types with the same interpolation points (red), resulting in different normalized position and velocity trajectories. Cubic Hermite splines exhibit a lower variance than quadratic and cubic splines, resulting in finer sampling granularity.
• Figure 4: The nominal trajectory (black) evolves through spline control points that are updated iteratively. New perturbed spline points are sampled around the nominal points with annealing noise according to Eq. \ref{['Eqn:overall-noise-kernel']}.