Bipedal walking and push recovery with a stepping strategy based on time-projection control

Abstract

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.

Scalable Closed-Form Trajectories for Periodic and Non-Periodic Human-Like Walking

“…that allows the user to change subject/gait parameters as well as to test transient conditions 1 . A C++ implementation of the 3LP model and the time-projection controller is also available for robotic applications [Faraji et al 2018b]. These codes only contain pure mathematic formulas in closed-form.…”

From standing balance to walking: A single control structure for a continuum of gaits

“…We note that even though COMAN is equipped with built-in torque control (i.e., a feedback loop on torque), because of hardware issues we did not use this functionality. Instead, voltage commands in open-loop models of DC motors were sent to the robot to approximately achieve the desired torque outputs (for more details on the voltage control, see Faraji et al (2018)).…”

A Dynamical System Approach for Adaptive Grasping, Navigation and Co-Manipulation with Humanoid Robots

“…To provide compliant walking for a position-controlled robot we use the time-projection foot-stepping controller [19], [21]. In this method, the robot naturally steps in-place by regulating the CoM on top of the ankle joints (to minimize the ankle torques).…”

“…By predicting future steps using a simplified model of the robot called 3LP [20], our method calculates plausible next footstep locations to capture the fall and restore balance. The 3LP model takes both stance and swing dynamics into account and can produce faster motions [21] compared to other push-recovery methods in the literature [22], [23]. With this algorithm, external forces can move the robot in any direction while foot-placement resists moderately.…”