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]

Imprecise dynamic walking with time-projection control

We present a new walking foot-placement controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of the 3LP model, our proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. This control paradigm reacts to disturbances immediately and includes rules to account for swing dynamics and leg-retraction. We apply it to a simulated Atlas robot in position-control, always commanded to perform in-place walking. The stance hip joint in our robot keeps the torso upright to let the robot naturally fall, and the swing hip joint tracks the desired footstep location. Combined with simple Center of Pressure (CoP) damping rules in the low-level controller, our foot-placement enables the robot to recover from strong pushes and produce periodic walking gaits when subject to persistent sources of disturbance, externally or internally. These gaits are imprecise, i.e., emergent from asymmetry sources rather than precisely imposing a desired velocity to the robot. Also in extreme conditions, restricting linearity assumptions of the 3LP model are often violated, but the system remains robust in our simulations. An extensive analysis of closed-loop eigenvalues, viable regions and sensitivity to push timings further demonstrate the strengths of our simple controller

Push recovery with stepping strategy based on time-projection control

In this paper, we present a simple control framework for on-line push recovery with dynamic stepping properties. Due to relatively heavy legs in our robot, we need to take swing dynamics into account and thus use a linear model called 3LP which is composed of three pendulums to simulate swing and torso dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use a particular time-projection method to adjust the next footstep location on-line during the motion continuously. This adjustment, which is found based on both pelvis and swing foot tracking errors, naturally takes the swing dynamics into account. Suggested adjustments are added to the Cartesian 3LP gaits and converted to joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies also ensure enough ground clearance in perturbed walking conditions. The proposed structure is robust, yet uses very simple state estimation and basic position tracking. We rely on the physical series elastic actuators to absorb impacts while introducing simple laws to compensate their tracking bias. Extensive experiments demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness due to relatively soft springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our proposed architecture.Comment: 20 pages journal pape

Push Recovery of a Position-Controlled Humanoid Robot Based on Capture Point Feedback Control

In this paper, a combination of ankle and hip strategy is used for push recovery of a position-controlled humanoid robot. Ankle strategy and hip strategy are equivalent to Center of Pressure (CoP) and Centroidal Moment Pivot (CMP) regulation respectively. For controlling the CMP and CoP we need a torque-controlled robot, however most of the conventional humanoid robots are position controlled. In this regard, we present an efficient way for implementation of the hip and ankle strategies on a position controlled humanoid robot. We employ a feedback controller to compensate the capture point error. Using our scheme, a simple and practical push recovery controller is designed which can be implemented on the most of the conventional humanoid robots without the need for torque sensors. The effectiveness of the proposed approach is verified through push recovery experiments on SURENA-Mini humanoid robot under severe pushes

Torque-Controlled Stepping-Strategy Push Recovery: Design and Implementation on the iCub Humanoid Robot

One of the challenges for the robotics community is to deploy robots which can reliably operate in real world scenarios together with humans. A crucial requirement for legged robots is the capability to properly balance on their feet, rejecting external disturbances. iCub is a state-of-the-art humanoid robot which has only recently started to balance on its feet. While the current balancing controller has proved successful in various scenarios, it still misses the capability to properly react to strong pushes by taking steps. This paper goes in this direction. It proposes and implements a control strategy based on the Capture Point concept [1]. Instead of relying on position control, like most of Capture Point related approaches, the proposed strategy generates references for the momentum-based torque controller already implemented on the iCub, thus extending its capabilities to react to external disturbances, while retaining the advantages of torque control when interacting with the environment. Experiments in the Gazebo simulator and on the iCub humanoid robot validate the proposed strategy

Walking Stabilization Using Step Timing and Location Adjustment on the Humanoid Robot, Atlas

While humans are highly capable of recovering from external disturbances and uncertainties that result in large tracking errors, humanoid robots have yet to reliably mimic this level of robustness. Essential to this is the ability to combine traditional "ankle strategy" balancing with step timing and location adjustment techniques. In doing so, the robot is able to step quickly to the necessary location to continue walking. In this work, we present both a new swing speed up algorithm to adjust the step timing, allowing the robot to set the foot down more quickly to recover from errors in the direction of the current capture point dynamics, and a new algorithm to adjust the desired footstep, expanding the base of support to utilize the center of pressure (CoP)-based ankle strategy for balance. We then utilize the desired centroidal moment pivot (CMP) to calculate the momentum rate of change for our inverse-dynamics based whole-body controller. We present simulation and experimental results using this work, and discuss performance limitations and potential improvements