Integration of vertical COM motion and angular momentum in an extended Capture Point tracking controller for bipedal walking

In this paper, we demonstrate methods for bipedal walking control based on the Capture Point (CP) methodology. In particular, we introduce a method to intuitively derive a CP reference trajectory from the next three steps and extend the linear inverted pendulum (LIP) based CP tracking controller introduced in [1], generalizing it to a model that contains vertical CoM motions and changes in angular momentum. Respecting the dynamics of general multibody systems, we propose a measurement-based compensation of multi-body effects, which leads to a stable closed-loop dynamics of bipedal walking robots. In addition we propose a ZMP projection method, which prevents the robots feet from tilting and ensures the best feasible CP tracking. The extended CP controller’s performance is validated in OpenHRP3 [2] simulations and compared to the controller proposed in [1]

A method for rough terrain locomotion based on Divergent Component of Motion

Abstract—For humanoid robots to be used in real world scenarios, there is a need of robust and simple walking controllers. Limitation to flat terrain is a drawback of many walking controllers. We overcome this limitation by extending the concept of Divergent Component of Motion (DCM, also called ‘Capture Point’) to 3D. Therefor, we introduce the “Enhanced Centroidal Moment Pivot point” (eCMP) and the “Virtual Repellent Point” (VRP), which allow for a very intuitive understanding of the robot’s CoM dynamics. Based on eCMP, VRP and DCM, we present a method for real-time planning and control of DCM trajectories in 3D

Analytical Center of Mass Trajectory Generation for Humanoid Walking and Running with Continuous Gait Transitions

We present an analytical trajectory generation framework for the combined computation of multiple walking and running sequences with continuous gait transitions. This framework builds on the Divergent Component of Motion (DCM)-based walking algorithm and the spline-based trajectory generation of the Biologically Inspired Deadbeat (BID) control for running. We describe our approach to generating closed-form center of mass (CoM) trajectories for walking and running by alternately linking the two gaits through continuity constraints. Thereby, we distinguish between vertical and horizontal planning. The vertical trajectory is computed in a forward recursion from the first to the last gait sequence. Due to the coupling of the gait sequences in the horizontal direction, we show the efficient generation of the horizontal CoM trajectory in a single matrix calculation. Subsequently, we unify the control strategies using a DCM tracking controller for the complete trajectory and integrate the proposed framework into an inverse dynamics-based whole-body controller. Finally, the presented approaches are validated in simulations with the humanoid robot Toro

Sensitivity of Legged Balance Control to Uncertainties and Sampling Period

We propose to quantify the effect of sensor and actuator uncertainties on the control of the center of mass and center of pressure in legged robots, since this is central for maintaining their balance with a limited support polygon. Our approach is based on robust control theory, considering uncertainties that can take any value between specified bounds. This provides a principled approach to deciding optimal feedback gains. Surprisingly, our main observation is that the sampling period can be as long as 200 ms with literally no impact on maximum tracking error and, as a result, on the guarantee that balance can be maintained safely. Our findings are validated in simulations and experiments with the torquecontrolled humanoid robot Toro developed at DLR. The proposed mathematical derivations and results apply nevertheless equally to biped and quadruped robots

Trajectory generation for continuous leg forces during double support and heel-to-toe shift based on divergent component of motion

This paper works with the concept of Divergent Component of Motion (DCM), also called ’(instantaneous) Capture Point’. We present two real-time DCM trajectory generators for uneven (three-dimensional) ground surfaces, which lead to continuous leg (and corresponding ground reaction) force profiles and facilitate the use of toe-off motion during double support. Thus, the resulting DCM trajectories are well suited for real-world robots and allow for increased step length and step height. The performance of the proposed methods was tested in numerous simulations and experiments on IHMC’s Atlas robot and DLR’s humanoid robot TORO

Sensitivity of Legged Balance Control to Uncertainties and Sampling Period

We propose to quantify the effect of sensor and actuator uncertainties on the control of the center of mass and center of pressure in legged robots, since this is central for maintaining their balance with a limited support polygon. Our approach is based on robust control theory, considering uncertainties that can take any value between specified bounds. This provides a principled approach to deciding optimal feedback gains. Surprisingly, our main observation is that the sampling period can be as long as 200 ms with literally no impact on maximum tracking error and, as a result, on the guarantee that balance can be maintained safely. Our findings are validated in simulations and experiments with the torquecontrolled humanoid robot Toro developed at DLR. The proposed mathematical derivations and results apply nevertheless equally to biped and quadruped robots

3D locomotion based on Divergent Component of Motion

Two-page abstract of a talk about the extension of the concept of Divergent Component of Motion (a.k.a. "Capture Point") to 3D

Online Learning of Centroidal Angular Momentum Towards Enhancing DCM-Based Locomotion

Gait generation frameworks for humanoid robots typically assume a constant centroidal angular momentum (CAM) throughout the walking cycle, which induces undesirable contact torques in the feet and results in performance degradation. In this work, we present a novel algorithm to learn the CAM online and include the obtained knowledge within the closed-form solutions of the Divergent Component of Motion (DCM) locomotion framework. To ensure a reduction of the contact torques at the desired center of pressure position, a CAM trajectory is generated and explicitly tracked by a whole-body controller. Experiments with the humanoid robot TORO demonstrate that the proposed method substantially increases the maximum step length and walking speed during locomotion