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

Trajectory Tracking Using Adaptive Fractional PID Control of Biped Robots with Time-Delay Feedback

This paper presents the application of fractional order time-delay adaptive neural networks to the trajectory tracking for chaos synchronization between Fractional Order delayed plant, reference and fractional order time-delay adaptive neural networks. For this purpose, we obtained two control laws and laws of adaptive weights online, obtained using the fractional order Lyapunov-Krasovskii stability analysis methodology. The main methodologies, on which the approach is based, are fractional order PID the fractional order Lyapunov-Krasovskii functions methodology, although the results we obtain are applied to a wide class of non-linear systems, we will apply it in this chapter to a bipedal robot. The structure of the biped robot is designed with two degrees of freedom per leg, corresponding to the knee and hip joints. Since torso and ankle are not considered, it is obtained a 4-DOF system, and each leg, we try to force this biped robot to track a reference signal given by undamped Duffing equation. To verify the analytical results, an example of dynamical network is simulated, and two theorems are proposed to ensure the tracking of the nonlinear system. The tracking error is globally asymptotically stabilized by two control laws derived based on a Lyapunov-Krasovskii functional

Finite-time disturbance reconstruction and robust fractional-order controller design for hybrid port-Hamiltonian dynamics of biped robots

In this paper, disturbance reconstruction and robust trajectory tracking control of biped robots with hybrid dynamics in the port-Hamiltonian form is investigated. A new type of Hamiltonian function is introduced, which ensures the finite-time stability of the closed-loop system. The proposed control system consists of two loops: an inner and an outer loop. A fractional proportional-integral-derivative filter is used to achieve finite-time convergence for position tracking errors at the outer loop. A fractional-order sliding mode controller acts as a centralized controller at the inner-loop, ensuring the finite-time stability of the velocity tracking error. In this loop, the undesired effects of unknown external disturbance and parameter uncertainties are compensated using estimators. Two disturbance estimators are envisioned. The former is designed using fractional calculus. The latter is an adaptive estimator, and it is constructed using the general dynamic of biped robots. Stability analysis shows that the closed-loop system is finite-time stable in both contact-less and impact phases. Simulation studies on two types of biped robots (i.e., two-link walker and RABBIT biped robot) demonstrate the proposed controller's tracking performance and disturbance rejection capability

Simulating Adaptive Human Bipedal Locomotion Based on Phase Resetting Using Foot-Contact Information

Humans generate bipedal walking by cooperatively manipulating their complicated and redundant musculoskeletal systems to produce adaptive behaviors in diverse environments. To elucidate the mechanisms that generate adaptive human bipedal locomotion, we conduct numerical simulations based on a musculoskeletal model and a locomotor controller constructed from anatomical and physiological findings. In particular, we focus on the adaptive mechanism using phase resetting based on the foot-contact information that modulates the walking behavior. For that purpose, we first reconstruct walking behavior from the measured kinematic data. Next, we examine the roles of phase resetting on the generation of stable locomotion by disturbing the walking model. Our results indicate that phase resetting increases the robustness of the walking behavior against perturbations, suggesting that this mechanism contributes to the generation of adaptive human bipedal locomotion

Stable Bilateral Teleoperation Control Method for Biped Robots with Time-Varying Delays

This document proposes a control scheme applied to delayed bilateral teleoperation of the forward and turn speed of a biped robot against asymmetric and time-varying delays. This biped robot is modeled as a hybrid dynamic system because it behaves as a continuous system when the leg moves forward and discrete when the foot touches the ground generating an impulsive response. It is proposed to vary online the damping according to the time delay present in the communication channel, and the walking cycle time using an optimization criterion, to decrease the teleoperation system errors. To accomplish this, a three-phase cascade calibration process is used, and their benefits are evidenced in a comparative simulation study. The first phase is an offline calibration of the inverse dynamic compensation and also the parameters of the bilateral controller. The second phase guarantees the bilateral coordination of the delayed teleoperation system, using the Lyapunov–Krasovskii stability theory, by changing the leader damping and the equivalent follower damping together. The third phase assures a stable walk of the hybrid dynamics by controlling the walking cycle time and the real damping to move the eigenvalues of the Poincaré map, numerically computed, to stable limit cycles and link this result with an equivalent continuous system to join both phases. Additionally, a fictitious force was implemented to detect and avoid possible collisions with obstacles. Finally, an intercontinental teleoperation experiment of an NAO robot via the Internet including force and visual feedback is shown