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 cubic Hermite 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 enables real-time control on standard CPU hardware, eliminating the GPU acceleration typically required by other state-of-the-art MPPI methods. We validate our approach on the Go2 quadrupedal robot, demonstrating a range of 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.

翻译：我们提出了一种基于采样的模型预测控制（MPC）框架，该框架无需依赖手工设计的步态模式或预定义的接触序列，即可实现涌现式运动。我们的方法仅通过高级目标的优化，就能发现从慢跑到疾驰的多样化运动模式、鲁棒的站立策略、跳跃以及倒立平衡。在模型预测路径积分（MPPI）基础上，我们提出了一种基于位置和速度控制点的三次埃尔米特样条参数化方法。该方法使接触建立与解除策略能够自动适应任务需求，且仅需有限数量的采样轨迹。这种样本效率使得在标准CPU硬件上即可实现实时控制，无需像其他前沿MPPI方法那样依赖GPU加速。我们在Go2四足机器人上验证了该方法，展示了多种涌现步态与基础跳跃能力。在仿真环境中，我们进一步展示了更复杂的行为，如后空翻、动态倒立平衡以及类人机器人的运动，所有这些均无需参考跟踪或离线预训练。