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Inventions 2016, 1(1), 7; doi:10.3390/inventions1010007

Modeling, Simulation and Control of the Walking of Biped Robotic Devices, Part II: Rectilinear Walking

Control and Computer Engineering Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10124 Torino, Italy
These authors contributed equally to this work.
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Academic Editor: Chien-Hung Liu
Received: 24 November 2015 / Revised: 2 March 2016 / Accepted: 7 March 2016 / Published: 22 March 2016
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Abstract

This is the second part of a three-part paper. It extends to the free walking results of a previous work on postural equilibrium of a lower limb exoskeleton for rehabilitation exercises. A classical approach has been adopted to design gait (zero moment point (ZMP), linearized inverted pendulum theory, inverse kinematics obtained through the pseudo-inverse of Jacobian matrices). While several ideas exploited here can be found in other papers of the literature, e.g., whole-body coordination, our contribution is the simplicity of the whole control approach that originates logically from a common root. (1) The approximation of the unilateral foot/feet-ground contacts with non-holonomic constraints leads naturally to a modeling and control design that implements a two-phase switching system. The approach is facilitated by Kane’s method and tools as described in Part I. (2) The Jacobian matrix is used to transfer from the Cartesian to the joint space a greater number of variables for redundancy than the degrees of freedom (DOF). We call it the extended Jacobian matrix. Redundancy and the prioritization of postural tasks is approached with weighted least squares. The singularity of the kinematics when knees are fully extended is solved very simply by fake knee joint velocities. (3) Compliance with the contact and accommodation of the swing foot on an uneven ground, when switching from single to double stance, and the transfer of weight from one foot to the other in double stance are approached by exploiting force/torque expressions returned from the constraints. (4) In the center of gravity (COG)/ZMP loop for equilibrium, an extended estimator, based on the linearized inverted pendulum, is adopted to cope with external force disturbances and unmodeled dynamics. Part II treats rectilinear walking, while Part III discusses turning while walking. View Full-Text
Keywords: humanoid robots; rehabilitation robotics; legged robots; human-like walk; active toe joints; preview control; postural equilibrium humanoid robots; rehabilitation robotics; legged robots; human-like walk; active toe joints; preview control; postural equilibrium
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Menga, G.; Ghirardi, M. Modeling, Simulation and Control of the Walking of Biped Robotic Devices, Part II: Rectilinear Walking. Inventions 2016, 1, 7.

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