Contingency Model Predictive Control for Stabilizing Bipedal Locomotion on Moving Surfaces

Core Concepts

A contingency model predictive control (CMPC) framework is presented to stabilize bipedal locomotion on dynamically moving surfaces by incorporating the "worst-case" predictive motion of the moving surface.

Abstract

The paper presents a contingency model predictive control (CMPC) approach for stabilizing bipedal locomotion on moving surfaces. The key highlights are:

The bipedal walker is modeled using a linear inverted pendulum (LIP) model, with the motion of the moving surface treated as an unknown disturbance.

The CMPC framework is developed to incorporate the "worst-case" predictive motion of the moving surface within the control horizon. This is achieved by computing bounded ranges of the surface acceleration and jerk, and formulating the CMPC optimization problem with equality constraints to ensure the control inputs can handle these extreme scenarios.

The CMPC design includes stability constraints based on the divergent component of motion (DCM) to ensure the convergence of the unstable mode of the LIP model.

Simulation results demonstrate that the proposed CMPC approach can successfully stabilize the bipedal walker on moving surfaces with various motion profiles, including sinusoidal and random disturbances, outperforming a regular model predictive control (MPC) approach.

The CMPC framework provides a less conservative and computationally efficient solution compared to other robust MPC approaches, while guaranteeing the walking stability under the anticipated uncertainties of the moving surface.

Stats

The linear inverted pendulum (LIP) model parameters include: l = 26 cm, ω = 6.14 rad/s.
The bipedal robot's foot strike length is set as sx = 5 cm and sy = 10 cm in the x and y directions, respectively.
The foot size is dx × dy = 2 × 2 cm.
The total walking cycle period is T = 0.3 s, with a 2:1 ratio between single-stance and double-stance phases.
The control horizon is Tc = 1 s, with N = 100 discretization steps.
The bounds on the surface acceleration jerk are jmin = -1 m/s^3, jmax = 1 m/s^3 for the x-direction, and jmin = -2 m/s^3, jmax = 2 m/s^3 for the y-direction.

Quotes

None.

Key Insights Distilled From

Contingency Model Predictive Control for Bipedal Locomotion on Moving Surfaces with a Linear Inverted Pendulum Model

by Kuo Chen,Xin... at arxiv.org 04-22-2024

https://arxiv.org/pdf/2404.12455.pdf

Deeper Inquiries

How can the CMPC framework be extended to handle more complex surface motion profiles, such as those with discontinuities or non-periodic patterns

To extend the Contingency Model Predictive Control (CMPC) framework to handle more complex surface motion profiles, such as those with discontinuities or non-periodic patterns, several adjustments and enhancements can be made:

Adaptive Prediction Horizon: The prediction horizon in the CMPC can be dynamically adjusted based on the characteristics of the surface motion. For non-periodic or discontinuous profiles, the horizon can be modified to capture sudden changes or irregular patterns effectively.

Incorporating Learning Algorithms: Machine learning algorithms can be integrated into the CMPC framework to adapt and learn from the surface motion patterns over time. This adaptive learning can help the controller anticipate and respond to various types of surface disturbances.

Hybrid Models: Combining the LIP model with more complex models that account for discontinuities or non-periodic patterns can provide a more accurate representation of the bipedal locomotion dynamics. Hybrid models can capture a wider range of surface motion scenarios.

Robust Optimization Techniques: Utilizing robust optimization techniques can enhance the CMPC's ability to handle uncertainties and variations in surface motion profiles. Robust optimization methods can ensure stability and performance under diverse conditions.

What are the potential limitations of the LIP model in accurately capturing the dynamics of bipedal locomotion on moving surfaces, and how can the CMPC approach be adapted to incorporate more detailed whole-body models

The Linear Inverted Pendulum (LIP) model, while effective for simplifying bipedal locomotion dynamics, has limitations in accurately capturing all aspects of the complex motion on moving surfaces. Some potential limitations of the LIP model include:

Limited Representation: The LIP model oversimplifies the dynamics of bipedal walking by assuming a point-mass model with fixed height. It may not capture the full-body dynamics, including joint movements and interactions with the environment.

Neglecting Multi-Contact Scenarios: The LIP model does not account for scenarios where the robot may have multiple contacts with the ground simultaneously, which can occur on uneven or moving surfaces.

To adapt the CMPC approach to incorporate more detailed whole-body models, the following strategies can be considered:

Multi-Body Dynamics: Integrating multi-body dynamics models that consider the full-body structure of the robot, including joint constraints, contact forces, and compliance, can provide a more realistic representation of bipedal locomotion.

Contact Modeling: Incorporating contact models that account for friction, compliance, and non-rigid interactions with the ground can improve the accuracy of the control strategy on moving surfaces.

Sensor Fusion: Utilizing sensor fusion techniques to integrate data from various sensors, such as IMUs, force sensors, and vision systems, can provide more comprehensive information for the control algorithm to adapt to the dynamic environment.

Can the CMPC approach be integrated with adaptive foot placement strategies to further enhance the stability and robustness of bipedal locomotion on moving surfaces

Integrating the CMPC approach with adaptive foot placement strategies can significantly enhance the stability and robustness of bipedal locomotion on moving surfaces. Here's how this integration can be beneficial:

Real-Time Adjustment: Adaptive foot placement strategies can dynamically adjust the foot position based on the predicted surface motion and the robot's state. This real-time adjustment can help maintain stability and prevent falls on unpredictable surfaces.

Optimal ZMP Generation: By combining adaptive foot placement with CMPC, the controller can optimize the Zero Moment Point (ZMP) trajectory to ensure stable walking by adjusting the foot placement to counteract disturbances in real-time.

Enhanced Resilience: Adaptive foot placement can improve the robot's resilience to external disturbances by actively responding to changes in the surface conditions. This adaptability can enhance the overall performance and agility of the bipedal robot on moving surfaces.