Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to induce a low dimensional system, the zero dynamics, that captures the underactuated aspects of a robot's model, without any approximations. To enhance intuition, the relation between physical constraints and virtual constraints is first established. From here, the hybrid zero dynamics of an underactuated bipedal model is developed, and its fundamental role in the design of asymptotically stable walking motions is established. The chapter includes numerous references to robots on which the highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte

Generación de trayectorias para un robot bípedo en fase de balanceo a partir de captura de movimiento humano

This paper proposes human motion capture to generate movements for the right leg in swing phase of a biped robot restricted to the sagittal plane -- Such movements are defined by time functions representing the desired angular positions for the joints involved -- Motion capture performed with a Microsoft Kinect TM camera and from the data obtained joint trajectories were generated to control the robot’s right leg in swing phase -- The proposed control law is a hybrid strategy; the first strategy is based on a computed torque control to track reference trajectories, and the second strategy is based on time scaling control ensuring the robot’s balance -- This work is a preliminary study to generate humanoid robot trajectories from motion captureEn este trabajo se propone la captura de movimiento humano para generar movimientos de la pierna derecha en fase de oscilación de un robot bípedo restringido al plano sagital -- Estos movimientos son definidos mediante funciones de tiempo que representan las posiciones angulares deseadas para las articulaciones involucradas -- La captura de movimiento realiza con un sensor Kinect TM y a partir de los datos obtenidos se generaron trayectorias articulares para controlar la pierna derecha del robot en la fase de balanceo -- La ley de control propuesta es una estrategia híbrida; la primera estrategia se basa en un control por par calculado para realizar un seguimiento de trayectorias de referencia, y la segunda estrategia se basa en un control por escalado de tiempo para garantizar el equilibrio del robot -- Este trabajo es un estudio preliminar para generar trayectorias de robots humanoides a partir de captura de movimient

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

Adaptive Excitation Control for the Underactuated Biped Robot

AbstractA control method to make the chaotic gait converge to a stable cycle gait is proposed for the biped robot with knees. This control method is called adaptive excitation control. It is based on the principle of bionics and the principle of self-excited. The control law is a combination of sinusoidal input and sensory feedback control. The control torque is only inputted into the robot's hip. Therefore, the walking process is low energy consuming. Simulation results show that the control method proposed in this paper is effective. It can enlarge the basin of attraction of limit cycle and increase the gait stability