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]

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

A Reactive and Efficient Walking Pattern Generator for Robust Bipedal Locomotion

Available possibilities to prevent a biped robot from falling down in the presence of severe disturbances are mainly Center of Pressure (CoP) modulation, step location and timing adjustment, and angular momentum regulation. In this paper, we aim at designing a walking pattern generator which employs an optimal combination of these tools to generate robust gaits. In this approach, first, the next step location and timing are decided consistent with the commanded walking velocity and based on the Divergent Component of Motion (DCM) measurement. This stage which is done by a very small-size Quadratic Program (QP) uses the Linear Inverted Pendulum Model (LIPM) dynamics to adapt the switching contact location and time. Then, consistent with the first stage, the LIPM with flywheel dynamics is used to regenerate the DCM and angular momentum trajectories at each control cycle. This is done by modulating the CoP and Centroidal Momentum Pivot (CMP) to realize a desired DCM at the end of current step. Simulation results show the merit of this reactive approach in generating robust and dynamically consistent walking patterns

Methodology for Zero-moment Point Experimental Modeling in the Frequency Domain

Frequency domain methodology is applied to obtain a nominal model for the Zero-Moment Point (ZMP) stability index of a biped robot in an attempt to establish a relationship between the robot trunk trajectories and the stability margin of the contact surface of the foot (or feet) touching the supporting soil. To this end the biped robot trunk is excited with a variable frequency sinusoidal signal around several operating points. These input oscillations generate other output oscillations that can be analyzed with the help of the ZMP measurement system. The proposed ZMP modeling approach not only considers classical rigid body model uncertainties but also non-modelled robot mechanical structure vibration modes. The non-linear ZMP model is obtained following three consecutive stages: Equivalent inverted pendulum dynamics, where saturation and acceleration upper bounds are taken into account, non-modelled inverted pendulum dynamics, including non-linear effects, and low-pass dynamics defining the system cut-off frequency. The effectiveness of this method is demonstrated in practice with the SILO2 biped robot prototype, and a simple control strategy is implemented in order to validate experimentally the usefulness of the models developed.Frequency domain methodology is applied to obtain a nominal model for the Zero-Moment Point (ZMP) stability index of a biped robot in an attempt to establish a relationship between the robot trunk trajectories and the stability margin of the contact surface of the foot (or feet) touching the supporting soil. To this end the biped robot trunk is excited with a variable frequency sinusoidal signal around several operating points. These input oscillations generate other output oscillations that can be analyzed with the help of the ZMP measurement system. The proposed ZMP modeling approach not only considers classical rigid body model uncertainties but also non-modelled robot mechanical structure vibration modes. The non-linear ZMP model is obtained following three consecutive stages: Equivalent inverted pendulum dynamics, where saturation and acceleration upper bounds are taken into account, non-modelled inverted pendulum dynamics, including non-linear effects, and low-pass dynamics defining the system cut-off frequency. The effectiveness of this method is demonstrated in practice with the SILO2 biped robot prototype, and a simple control strategy is implemented in order to validate experimentally the usefulness of the models developed

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

Orbit Characterization, Stabilization and Composition on 3D Underactuated Bipedal Walking via Hybrid Passive Linear Inverted Pendulum Model

A Hybrid passive Linear Inverted Pendulum (H-LIP) model is proposed for characterizing, stabilizing and composing periodic orbits for 3D underactuated bipedal walking. Specifically, Period-l (P1) and Period -2 (P2) orbits are geometrically characterized in the state space of the H-LIP. Stepping controllers are designed for global stabilization of the orbits. Valid ranges of the gains and their optimality are derived. The optimal stepping controller is used to create and stabilize the walking of bipedal robots. An actuated Spring-loaded Inverted Pendulum (aSLIP) model and the underactuated robot Cassie are used for illustration. Both the aSLIP walking with PI or P2 orbits and the Cassie walking with all 3D compositions of the PI and P2 orbits can be smoothly generated and stabilized from a stepping-in-place motion. This approach provides a perspective and a methodology towards continuous gait generation and stabilization for 3D underactuated walking robots