Variable Horizon MPC with Swing Foot Dynamics for Bipedal Walking Control (2010.08198v2)

Abstract: In this paper, we present a novel two-level variable Horizon Model Predictive Control (VH-MPC) framework for bipedal locomotion. In this framework, the higher level computes the landing location and timing (horizon length) of the swing foot to stabilize the unstable part of the center of mass (CoM) dynamics, using feedback from the CoM states. The lower level takes into account the swing foot dynamics and generates dynamically consistent trajectories for landing at the desired time as close as possible to the desired location. To do that, we use a simplified model of the robot dynamics projected in swing foot space that takes into account joint torque constraints as well as the friction cone constraints of the stance foot. We show the effectiveness of our proposed control framework by implementing robust walking patterns on our torque-controlled and open-source biped robot, Bolt. We report extensive simulations and real robot experiments in the presence of various disturbances and uncertainties.

• The paper introduces a two-level VH-MPC framework that decouples high-level CoM motion from low-level swing foot trajectory planning.
• It employs a linearized model for swing foot dynamics that adheres to joint torque and friction constraints, ensuring feasible optimization.
• Simulations on the Bolt robot demonstrate enhanced balance and robustness, maintaining real-time performance under various disturbances.

An Overview of Variable Horizon MPC with Swing Foot Dynamics for Bipedal Walking Control

The paper "Variable Horizon MPC with Swing Foot Dynamics for Bipedal Walking Control" introduces a two-level control framework employing Variable Horizon Model Predictive Control (VH-MPC) to enhance bipedal locomotion. By focusing on a modular design that considers both Center of Mass (CoM) dynamics and swing foot dynamics, the authors address the complex interaction dynamics of humanoid robots, particularly in uncertain and dynamically changing environments.

This work distinguishes itself by splitting the control problem into a high-level and a low-level MPC problem. The high-level VH-MPC is responsible for determining the optimal step location and timing based on the CoM's divergent component of motion (DCM), while the low-level MPC focuses on the trajectory planning of the swing foot to achieve the desired landing states. This division allows for a more manageable optimization problem, ensuring real-time compute efficiency, a critical requirement in robotic control.

Technical Contributions

1. Two-Level VH-MPC Framework: The primary innovation of this paper is the integration of a two-tiered VH-MPC structure. The high-level MPC adapts to DCM measurements, optimizing future contact points and the timing of these contacts. This is a critical advancement that allows the system to manage disturbances and uncertainties dynamically, without the need for a predefined trajectory.
2. Swing Foot Dynamics: The paper introduces a novel approach to calculate the swing foot trajectory. By projecting the robot dynamics into the swing foot space and accounting for joint torque and friction cone constraints, the authors develop a linearized model that simplifies the problem to a feasible linear optimization problem. This linearization is validated against more complex nonlinear behavior in simulations.
3. Real-World Simulations and Experiments: The effectiveness of the proposed framework is demonstrated through extensive simulations and experimental validation on the Bolt robot, showcasing robust walking patterns even under various disturbances such as uneven terrain, push recovery, and slippery surfaces. The results demonstrate that the robot can maintain balance and correct its trajectory dynamically.

Key Findings and Implications

• Control Precision: The paper highlights the VH-MPC's ability to precisely control step timing and landing location, leading to improved balance and adaptability in bipedal locomotion.
• Robustness Against Disturbances: By dynamically recalculating the step location and timing, the system proved its ability to handle unexpected disturbances, underpinning its application potential in real-world scenarios where terrains are unpredictable.
• Efficiency in Computation: The decomposition of the control problem into a high and low-level structure results in a lean optimization process, enhancing computational tractability. This, in turn, facilitates the potential real-time application of these control algorithms in humanoid robotics.

Speculations on Future Developments

Given the promising results showcased in this paper, future research may advance in several directions. The extension of this framework to accommodate running motions or 3D environments presents a significant avenue for exploration. Furthermore, integrating machine learning techniques for improved prediction of dynamic environments could enhance the adaptability and efficiency of VH-MPC frameworks. There is also interest in improving whole-body dynamics modeling to refine control systems further, particularly in more structurally complex humanoid robots. Integrating an event-based control approach, as hinted at in the paper, would also mitigate discontinuities in dynamic environments, offering steadier transitions during contact switches.

The two-level VH-MPC framework outlined in this paper provides a compelling demonstration of step dynamic adaptation and robust motion control for bipedal robots, setting a solid foundation for future enhancements in humanoid robotics maneuverability and environmental interaction.