We demonstrate the surprising real-world effectiveness of a very simple approach to whole-body model-predictive control (MPC) of quadruped and humanoid robots: the iterative LQR (iLQR) algorithm with MuJoCo dynamics and finite-difference approximated derivatives. Building upon the previous success of model-based behavior synthesis and control of locomotion and manipulation tasks with MuJoCo in simulation, we show that these policies can easily generalize to the real world with few sim-to-real considerations. Our baseline method achieves real-time whole-body MPC on a variety of hardware experiments, including dynamic quadruped locomotion, quadruped walking on two legs, and full-sized humanoid bipedal locomotion. We hope this easy-to-reproduce hardware baseline lowers the barrier to entry for real-world whole-body MPC research and contributes to accelerating research velocity in the community. Our code and experiment videos will be available online at:https://johnzhang3.github.io/mujoco_ilqr

The humanoid robot (Unitree G1) demonstrates diverse agile whole-body skills, showcasing the control policies' agility: (a) Cristiano Ronaldo's signature celebration involving a jump with a 180-degree mid-air rotation; (b) LeBron James's "Silencer" celebration involving single-leg balancing; and (c) Kobe Bryant's famous fadeaway jump shot involving single-leg jumping and landing; (d) 1.5m-forward jumping; (e) Leg stretching; (f) 1.3m-side jumping. Abstract -- Humanoid robots hold the potential for unparalleled versatility for performing human-like, whole-body skills. However, achieving agile and coordinated whole-body motions remains a significant challenge due to the dynamics mismatch between simulation and the real world. Existing approaches, such as system identification (SysID) and domain randomization (DR) methods, often rely on labor-intensive parameter tuning or result in overly conservative policies that sacrifice agility. In this paper, we present ASAP (Aligning Simulation and Real Physics), a two-stage framework designed to tackle the dynamics mismatch and enable agile humanoid whole-body skills. Then ASAP fine-tunes pre-trained policies with the delta action model integrated into the simulator to align effectively with real-world dynamics. We evaluate ASAP across three transfer scenarios--IsaacGym to IsaacSim, IsaacGym to Genesis, and IsaacGym to the real-world Unitree G1 humanoid robot. Our approach significantly improves agility and whole-body coordination across various dynamic motions, reducing tracking error compared to SysID, DR, and delta dynamics learning baselines. ASAP enables highly agile motions that were previously difficult to achieve, demonstrating the potential of delta action learning in bridging simulation and real-world dynamics. These results suggest a promising sim-to-real direction for developing more expressive and agile humanoids. I NTRODUCTION For decades, we have envisioned humanoid robots achieving or even surpassing human-level agility. However, most prior work [46, 74, 47, 73, 107, 19, 95, 50] has primarily focused on locomotion, treating the legs as a means of mobility. Recent studies [10, 25, 24, 26, 32] have introduced whole-body expressiveness in humanoid robots, but these efforts have primarily focused on upper-body motions and have yet to achieve the agility seen in human movement.

Due to high dimensionality and non-convexity, real-time optimal control using full-order dynamics models for legged robots is challenging. Therefore, Nonlinear Model Predictive Control (NMPC) approaches are often limited to reduced-order models. Sampling-based MPC has shown potential in nonconvex even discontinuous problems, but often yields suboptimal solutions with high variance, which limits its applications in high-dimensional locomotion. This work introduces DIAL-MPC (Diffusion-Inspired Annealing for Legged MPC), a sampling-based MPC framework with a novel diffusion-style annealing process. Such an annealing process is supported by the theoretical landscape analysis of Model Predictive Path Integral Control (MPPI) and the connection between MPPI and single-step diffusion. Algorithmically, DIAL-MPC iteratively refines solutions online and achieves both global coverage and local convergence. In quadrupedal torque-level control tasks, DIAL-MPC reduces the tracking error of standard MPPI by $13.4$ times and outperforms reinforcement learning (RL) policies by $50\%$ in challenging climbing tasks without any training. In particular, DIAL-MPC enables precise real-world quadrupedal jumping with payload. To the best of our knowledge, DIAL-MPC is the first training-free method that optimizes over full-order quadruped dynamics in real-time.

Recent advances in diffusion models have demonstrated their strong capabilities in generating high-fidelity samples from complex distributions through an iterative refinement process. Despite the empirical success of diffusion models in motion planning and control, the model-free nature of these methods does not leverage readily available model information and limits their generalization to new scenarios beyond the training data (e.g., new robots with different dynamics). In this work, we introduce Model-Based Diffusion (MBD), an optimization approach using the diffusion process to solve trajectory optimization (TO) problems without data. The key idea is to explicitly compute the score function by leveraging the model information in TO problems, which is why we refer to our approach as model-based diffusion. Moreover, although MBD does not require external data, it can be naturally integrated with data of diverse qualities to steer the diffusion process. We also reveal that MBD has interesting connections to sampling-based optimization. Empirical evaluations show that MBD outperforms state-of-the-art reinforcement learning and sampling-based TO methods in challenging contact-rich tasks. Additionally, MBD's ability to integrate with data enhances its versatility and practical applicability, even with imperfect and infeasible data (e.g., partial-state demonstrations for high-dimensional humanoids), beyond the scope of standard diffusion models.

Sampling-based Model Predictive Control (MPC) has been a practical and effective approach in many domains, notably model-based reinforcement learning, thanks to its flexibility and parallelizability. Despite its appealing empirical performance, the theoretical understanding, particularly in terms of convergence analysis and hyperparameter tuning, remains absent. In this paper, we characterize the convergence property of a widely used sampling-based MPC method, Model Predictive Path Integral Control (MPPI). We show that MPPI enjoys at least linear convergence rates when the optimization is quadratic, which covers time-varying LQR systems. We then extend to more general nonlinear systems. Our theoretical analysis directly leads to a novel sampling-based MPC algorithm, CoVariance-Optimal MPC (CoVO-MPC) that optimally schedules the sampling covariance to optimize the convergence rate. Empirically, CoVO-MPC significantly outperforms standard MPPI by 43-54% in both simulations and real-world quadrotor agile control tasks.

In this paper, we present a method to manipulate unknown objects in-hand using tactile sensing without relying on a known object model. In many cases, vision-only approaches may not be feasible; for example, due to occlusion in cluttered spaces. We address this limitation by introducing a method to reorient unknown objects using tactile sensing. It incrementally builds a probabilistic estimate of the object shape and pose during task-driven manipulation. Our approach uses Bayesian optimization to balance exploration of the global object shape with efficient task completion. To demonstrate the effectiveness of our method, we apply it to a simulated Tactile-Enabled Roller Grasper, a gripper that rolls objects in hand while collecting tactile data. We evaluate our method on an insertion task with randomly generated objects and find that it reliably reorients objects while significantly reducing the exploration time.