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

3LP: a linear 3D-walking model including torso and swing dynamics

In this paper, we present a new model of biped locomotion which is composed of three linear pendulums (one per leg and one for the whole upper body) to describe stance, swing and torso dynamics. In addition to double support, this model has different actuation possibilities in the swing hip and stance ankle which could be widely used to produce different walking gaits. Without the need for numerical time-integration, closed-form solutions help finding periodic gaits which could be simply scaled in certain dimensions to modulate the motion online. Thanks to linearity properties, the proposed model can provide a computationally fast platform for model predictive controllers to predict the future and consider meaningful inequality constraints to ensure feasibility of the motion. Such property is coming from describing dynamics with joint torques directly and therefore, reflecting hardware limitations more precisely, even in the very abstract high level template space. The proposed model produces human-like torque and ground reaction force profiles and thus, compared to point-mass models, it is more promising for precise control of humanoid robots. Despite being linear and lacking many other features of human walking like CoM excursion, knee flexion and ground clearance, we show that the proposed model can predict one of the main optimality trends in human walking, i.e. nonlinear speed-frequency relationship. In this paper, we mainly focus on describing the model and its capabilities, comparing it with human data and calculating optimal human gait variables. Setting up control problems and advanced biomechanical analysis still remain for future works.Comment: Journal paper under revie

Adaptive, fast walking in a biped robot under neuronal control and learning

Human walking is a dynamic, partly self-stabilizing process relying on the interaction of the biomechanical design with its neuronal control. The coordination of this process is a very difficult problem, and it has been suggested that it involves a hierarchy of levels, where the lower ones, e.g., interactions between muscles and the spinal cord, are largely autonomous, and where higher level control (e.g., cortical) arises only pointwise, as needed. This requires an architecture of several nested, sensori–motor loops where the walking process provides feedback signals to the walker's sensory systems, which can be used to coordinate its movements. To complicate the situation, at a maximal walking speed of more than four leg-lengths per second, the cycle period available to coordinate all these loops is rather short. In this study we present a planar biped robot, which uses the design principle of nested loops to combine the self-stabilizing properties of its biomechanical design with several levels of neuronal control. Specifically, we show how to adapt control by including online learning mechanisms based on simulated synaptic plasticity. This robot can walk with a high speed (> 3.0 leg length/s), self-adapting to minor disturbances, and reacting in a robust way to abruptly induced gait changes. At the same time, it can learn walking on different terrains, requiring only few learning experiences. This study shows that the tight coupling of physical with neuronal control, guided by sensory feedback from the walking pattern itself, combined with synaptic learning may be a way forward to better understand and solve coordination problems in other complex motor tasks

Controllability of kinematic control systems on stratified configuration spaces

This paper considers nonlinear kinematic controllability of a class of systems called stratified. Roughly speaking, such stratified systems have a configuration space which can be decomposed into submanifolds upon which the system has different sets of equations of motion. For such systems, considering controllability is difficult because of the discontinuous form of the equations of motion. The main result in this paper is a controllability test, analogous to Chow's theorem, is based upon a construction involving distributions, and the extension thereof to robotic gaits

Asimov's Coming Back

Ever since the word ‘ROBOT’ first appeared in a science\ud fiction in 1921, scientists and engineers have been trying\ud different ways to create it. Present technologies in\ud mechanical and electrical engineering makes it possible\ud to have robots in such places as industrial manufacturing\ud and assembling lines. Although they are\ud essentially robotic arms or similarly driven by electrical\ud power and signal control, they could be treated the\ud primitive pioneers in application. Researches in the\ud laboratories go much further. Interdisciplines are\ud directing the evolution of more advanced robots. Among these are artificial\ud intelligence, computational neuroscience, mathematics and robotics. These disciplines\ud come closer as more complex problems emerge.\ud From a robot’s point of view, three basic abilities are needed. They are thinking\ud and memory, sensory perceptions, control and behaving. These are capabilities we\ud human beings have to adapt ourselves to the environment. Although\ud researches on robots, especially on intelligent thinking, progress slowly, a revolution\ud for biological inspired robotics is spreading out in the laboratories all over the world

Eligibility Propagation to Speed up Time Hopping for Reinforcement Learning

A mechanism called Eligibility Propagation is proposed to speed up the Time Hopping technique used for faster Reinforcement Learning in simulations. Eligibility Propagation provides for Time Hopping similar abilities to what eligibility traces provide for conventional Reinforcement Learning. It propagates values from one state to all of its temporal predecessors using a state transitions graph. Experiments on a simulated biped crawling robot confirm that Eligibility Propagation accelerates the learning process more than 3 times.Comment: 7 page

Respiratory, postural and spatio-kinetic motor stabilization, internal models, top-down timed motor coordination and expanded cerebello-cerebral circuitry: a review

Human dexterity, bipedality, and song/speech vocalization in Homo are reviewed within a motor evolution perspective in regard to 

(i) brain expansion in cerebello-cerebral circuitry, 
(ii) enhanced predictive internal modeling of body kinematics, body kinetics and action organization, 
(iii) motor mastery due to prolonged practice, 
(iv) task-determined top-down, and accurately timed feedforward motor adjustment of multiple-body/artifact elements, and 
(v) reduction in automatic preflex/spinal reflex mechanisms that would otherwise restrict such top-down processes. 

Dual-task interference and developmental neuroimaging research argues that such internal modeling based motor capabilities are concomitant with the evolution of 
(vi) enhanced attentional, executive function and other high-level cognitive processes, and that 
(vii) these provide dexterity, bipedality and vocalization with effector nonspecific neural resources. 

The possibility is also raised that such neural resources could 
(viii) underlie human internal model based nonmotor cognitions. 
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