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🔥 Content Introduction
1. Technical Background: The 3D Scene Requirements for Robot Motion Control and the Limitations of Traditional DCM
In the motion control of complex robotic systems such as humanoid robots and quadrupedal robots, dynamic balance is a core technical challenge — robots need to adjust their limb postures and forces in real-time during actions like walking, turning, and climbing stairs to avoid tipping over. Traditional motion control methods are often based on 2D plane assumptions (e.g., only considering forward/backward and left/right directions), but in practical applications, robots often operate in 3D environments (e.g., walking on slopes, crossing height obstacles, working on uneven terrain), requiring them to simultaneously handle forces and motion changes in three dimensions: x (forward/backward), y (left/right), and z (up/down). 2D control methods struggle to meet the balance and trajectory accuracy requirements in 3D scenarios.
The Divergent Component of Motion (DCM), also known as the “Capture Point,” is a classic theory for dynamic balance control in robots. It describes the relationship between the robot’s center of mass (CoM) motion and the support area to assess motion stability — when the DCM is within the support polygon, the robot remains balanced; if it exceeds, it faces the risk of tipping over. However, traditional DCM is only applicable to 2D plane scenarios and has two major limitations: first, it cannot encode 3D force information, only handling gravity and ground support forces in the plane, making it difficult to cope with external forces along the z-axis in 3D environments (e.g., vertical collision forces, forces on slopes); second, it has insufficient trajectory generation capability, as traditional DCM trajectory generators can only output discrete support point positions and cannot generate continuous leg force profiles. Additionally, during the double support phase (e.g., when both feet are on the ground), it struggles to adapt to fine actions like toe-off, limiting the robot’s motion flexibility in complex 3D scenarios.
To address these issues, this study extends DCM theory to 3D space, proposing two core concepts: “Enhanced Center of Mass Moment Point (eCMP)” and “Virtual Repulsion Point (VRP),” enabling the encoding of the direction and magnitude of external forces and total forces (external forces + gravity) in 3D environments. This leads to the construction of a real-time planning and tracking control framework for robot DCM trajectories in 3D scenarios, providing technical support for stable robot motion in complex 3D environments.
⛳️ Operating Results
📣 Sample Code
function xi_d = get_xi_d(t, t_step, b, r_vrp, xi_eos)
xi_d = r_vrp + exp((1/b)*(t-t_step)).*(xi_eos – r_vrp);
end
🔗 References
Englsberger, Johannes, Christian Ott, and Alin Albu-Schäffer. “Three-dimensional bipedal walking control based on divergent component of motion.” IEEE Transactions on Robotics 31.2 (2015): 355-368.
🎈 Some theoretical references are from online literature; if there is any infringement, please contact the author for removal.
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