BiConMP: A Nonlinear Model Predictive Control Framework for Whole Body Motion Planning (2201.07601v2)

Abstract: Online planning of whole-body motions for legged robots is challenging due to the inherent nonlinearity in the robot dynamics. In this work, we propose a nonlinear MPC framework, the BiConMP which can generate whole body trajectories online by efficiently exploiting the structure of the robot dynamics. BiConMP is used to generate various cyclic gaits on a real quadruped robot and its performance is evaluated on different terrain, countering unforeseen pushes and transitioning online between different gaits. Further, the ability of BiConMP to generate non-trivial acyclic whole-body dynamic motions on the robot is presented. The same approach is also used to generate various dynamic motions in MPC on a humanoid robot (Talos) and another quadruped robot (AnYmal) in simulation. Finally, an extensive empirical analysis on the effects of planning horizon and frequency on the nonlinear MPC framework is reported and discussed.

• The paper introduces a novel biconvex dynamics solver using ADMM and FISTA to efficiently optimize centroidal dynamics.
• The framework achieves real-time closed-loop planning at 20Hz, enabling robust whole-body trajectory adaptation to disturbances.
• Extensive experiments on multiple platforms validate its effectiveness in dynamic tasks like trotting, jumping, and complex gestures.

Overview of "BiConMP: A Nonlinear Model Predictive Control Framework for Whole Body Motion Planning"

The paper presents BiConMP, an innovative nonlinear Model Predictive Control (MPC) framework designed for whole-body motion planning in legged robotic systems. The primary contribution is leveraging the inherent biconvex structure of the centroidal dynamics of robots to optimize trajectory generation in real-time. This work embodies a substantial advancement in legged robotics, demonstrating reliable and efficient motion planning across varied robotic platforms and environments.

Key Contributions

1. Biconvex Dynamics Solver: The paper proposes a novel method to exploit the biconvex nature of the centroidal dynamics optimization problem. The solver employs the Alternating Direction Method of Multipliers (ADMM) and Fast Iterative Shrinkage Thresholding Algorithm (FISTA) to effectively and efficiently solve the optimization problem by breaking it into two convex sub-problems. This allows the framework to meet real-time computation requirements.
2. Closed-Loop Nonlinear MPC: BiConMP is capable of re-planning whole-body trajectories in a receding-horizon fashion at a frequency of 20Hz, showing impressive robustness to unforeseen disturbances and terrain variations. This robust online adaptation capability is crucial for real-world robotic deployment.
3. Blue-Sky Experimentation: The research demonstrates the flexibility and effectiveness of BiConMP across various robotic platforms, including the Solo12 quadruped, the Talos humanoid, and the Anymal quadruped robot. It successfully generates diverse motions such as trotting, jumping, and performing intricate tasks like a high-five gesture in real-time.
4. Kino-Dynamic Decomposition: Building on the kino-dynamic separation approach, the framework solves the nonlinear dynamics and kinematic problems iteratively, ensuring that the whole-body motion plans are feasible and efficient. DDP-based solvers are deployed for full-body kinematics, facilitating the solution of high-dimensional and nonlinear optimization problems inherent in humanoid robotics.

Implications and Future Directions

The research advances practical and theoretical understanding in the domain of whole-body motion planning for legged robots by overcoming challenges related to nonlinear dynamics and computational constraints. Practically, the real-time re-planning capability promises improved adaptability of robotic systems in dynamic and unpredictable environments such as disaster zones or human interaction settings. Theoretically, the work offers a potential template for employing first-order optimization methods like proximal algorithms in robotics, which could influence future research on MPC frameworks for broader applications beyond legged locomotion.

Future avenues may include further optimization of the solve times, possibly through aggressive code optimization or machine learning-based warm-start strategies. Additionally, integrating torque constraints directly into the optimization pipeline and refining the interplay between different control layers stands as a potential area for further research.

Numerical Results

• The framework demonstrated real-time performance with solve times averaging 20-35ms per cycle, emphasizing its practical applicability.
• Analyzed across various gaits, the approach showed robustness to external perturbations and handled complex dynamic tasks effectively, validating the theoretical robustness claims with empirical evidence.

In conclusion, BiConMP constitutes a significant contribution towards enabling adaptive and resilient legged robotic systems, underpinned by sophisticated algorithmic innovation, and sets a promising groundwork for future explorations in the field of dynamic robot locomotion and control.