Reference-Free Sampling-Based Model Predictive Control

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.