Abstract
A biped robot is a mechanical multichain system. The peculiar features, that distinguishes this kind of robot with respect to others, e.g., industrial robots, is its switching nature between different phases, each one is the same mechanics subject to a different constraint. Moreover, because these (unilateral) constraints, represented by the contact between the foot/feet and the ground, play a fundamental role for maintaining the postural equilibrium during the gait, forces and torques returned must be continuously monitored, as they pose stringent conditions to the trajectories that the joints of the robot can safely follow. The advantages of using the Kane’s method to approach the dynamical model (models) of the system are outlined. This paper, divided in three parts, deals with a generical biped device, which can be an exoskeleton for rehabilitation or an indipendent robot. Part I is devoted to modelling and simulation, part II approaches the control of walk in a rectilinear trajectory, part III extends the results on turning while walking. In particular, this part I describes the model of the biped robot and the practicalities of building a computer simulator, leveraging on the facilities offered by the symbolic computational environment Autolev that complements the Kane’s method.
Highlights
A biped robot is a particular mechanical multichain system, which, as the time evolves, switches between phases, characterized by different constraints
This has several consequences: From a postural equilibrium point of view because these constraints, represented by the contact between the foot/feet and the ground, play a fundamental role for maintaining the postural equilibrium during the gait, their returned forces and torques pose stringent conditions to the trajectories that the joints of the robot can safely follow, and must be continuously monitored; From the robot control point of view the changing constraints modify the number of degrees of freedom (DOF) of the dynamics, that can result underactuaded or overactuaded depending on the ground contacts, and the controller itself must be a switching system
The authors have been involved for several years in modelling and control of biped robots for entertainment [1] and exoskeletons for postural rehabilitation [2], so they were faced from the Inventions 2016, 1, 6; doi:10.3390/inventions1010006
Summary
A biped robot is a particular mechanical multichain system, which, as the time evolves, switches between phases (single stance, double stance, each one divided by subphases), characterized by different constraints. The Kane’s method is complemented with a symbolic computational environment, originally called Autolev and MotionGenesis Kane 5.x [9], that generates all mathematical expressions needed for modelling and design controls, and produces prototypical source code in Fortran, Matlab or C of the equations in ordinary differential form (ODEs) even for non holonomical constrained systems, which can be simulated using standard solvers In this framework are available, expressions of a variety of mechanical quantities needed for the analysis, such as linearization matrices, kinematics, Jacobians, explicit reaction forces/torques from the constraints, kinetic energy, generalized impulses, generalized momentum, etc. The organization of Part I is as follows: a review of previous work, hybrid complementary dynamical systems, is presented in Section 2; in Section 3 a biped robot and its mechanical model is described; in Section 4 the general scheme of the simulator is presented
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