Real-Time Whole-Body Control of Legged Robots with Model-Predictive Path Integral Control (2409.10469v1)

Abstract: This paper presents a system for enabling real-time synthesis of whole-body locomotion and manipulation policies for real-world legged robots. Motivated by recent advancements in robot simulation, we leverage the efficient parallelization capabilities of the MuJoCo simulator to achieve fast sampling over the robot state and action trajectories. Our results show surprisingly effective real-world locomotion and manipulation capabilities with a very simple control strategy. We demonstrate our approach on several hardware and simulation experiments: robust locomotion over flat and uneven terrains, climbing over a box whose height is comparable to the robot, and pushing a box to a goal position. To our knowledge, this is the first successful deployment of whole-body sampling-based MPC on real-world legged robot hardware. Experiment videos and code can be found at: https://whole-body-mppi.github.io/

• The paper demonstrates a sampling-based predictive control method using MPPI to achieve real-time whole-body coordination on legged robots.
• It reduces computational complexity by employing cubic spline control points, smoothing torque commands via low-level PD controllers.
• Experimental results on a Unitree Go1 quadruped validate robust locomotion and manipulation across various terrains with emergent contact behaviors.

Real-Time Whole-Body Control of Legged Robots with Model-Predictive Path Integral Control

The paper "Real-Time Whole-Body Control of Legged Robots with Model-Predictive Path Integral Control" presents an advanced system to enable the real-time synthesis of locomotion and manipulation policies for legged robots. Leveraging the MuJoCo simulation engine's efficient parallelization, the authors implement model-predictive path integral control (MPPI) to achieve fast sampling over robot state and action trajectories, resulting in robust real-world locomotion and manipulation capabilities with a straightforward control strategy.

Key Contributions

1. Sampling-Based Predictive Control: This work demonstrates the first successful deployment of sampling-based predictive control in real-time on legged robots. The effectiveness of MPPI in solving high-dimensional tasks of locomotion and manipulation using merely a few design choices is thoroughly examined.
2. Reduction of Search Space: To ensure efficient computation, the authors use spline control representations by sampling over the control points of cubic splines in the robot's joint space. These control points guide low-level PD controllers to produce torque commands, significantly smoothing the controls.
3. Real-World and Simulation Experiments: A series of hardware and simulation experiments underpin the robustness of the proposed system. These include locomotion over flat and uneven terrains, box climbing, and pushing a box to target positions. Particularly noteworthy results include the emergent contact behaviors—like body pushes and leg kicks—not pre-specified in the control policies.

Experimental Results

The employed setup consists of a Unitree Go1 quadruped robot, with offboard controllers running on an Intel i9-12900KS CPU, interfaced via Ethernet and ROS. The control algorithm operates at a 100 Hz rate, planning over a 0.4 s horizon with 30 sample rollouts per iteration.

1. Locomotion on Flat Terrain: The MPPI policy enabled efficient trotting in place and walking to user-defined waypoints while being robust against moderate external disturbances.

2. Challenging Terrains: Scaling up in complexity, the robot successfully climbed over obstacles as tall as its standing height, demonstrating emergent motions like jumps and body contacts.

3. Object Manipulation: The robot's ability to push a box to various target locations with emergent behaviors such as body and shoulder contacts was validated through experiments with a success rate of 90% and 60% for different goal settings.

Insights from Ablation Studies

The authors performed ablation studies to dissect the impact of several key hyperparameters:

• Sampling Representation: Using cubic splines for control points yielded the best result compared to zeroth-order and linear interpolations.
• Control Frequency: Optimal performance plateaued around 100 Hz.
• Temperature Parameter ($\lambda$): The best performance was observed at $\lambda \approx 0.1$.
• Prediction Horizon: A horizon of 40-50 timesteps was found to be optimal.
• Number of Samples: Approximately 40 samples sufficed, beyond which additional samples did not significantly boost performance.

Comparative Analysis

The authors compare MPPI with traditional MPC and RL approaches. Unlike MPC, which requires model gradients for policy optimization, or RL, which involves extensive offline training, MPPI offers a solution to efficiently plan whole-body motions fully online. This makes it suitable for tasks where accurate full-body dynamics are essential but offline training is unfeasible.

Implications and Future Directions

The deployment of MPPI in real-world settings bridges the gap between accurate simulation and practical application. The system can generate complex contact-rich behaviors in real-time, presenting significant implications for deploying more sophisticated robotics in unstructured environments.

Future Research Directions:

1. Sim-to-Real Adaptations: Enhancing the model parameters through online updates can significantly reduce the performance gap observed on physical hardware.
2. Advanced Sampling Techniques: Implementation of more adaptive or sophisticated sampling techniques could improve the performance outputs.
3. Tool Integration: Integrating with MJPC software can facilitate user interactions, enabling easier task design and control parameter tuning.

Conclusion

The paper provides substantial groundwork for deploying sampling-based MPC on real-world robots, demonstrating that simple design choices combined with efficient simulation can address high-dimensional control problems previously reserved for offline RL. This work opens avenues for further research on adaptive control policies and practical applicability in diverse robotic applications.