Abstract
In part II of this group of papers, the control of the gait of a biped robot during rectilinear walk was considered. The modeling approach and simulation, using Kane’s method with implementation leveraged by Autolev, a symbolic computational environment that is complementary, was discussed in part I. Performing turns during the walk is technically more complex than the rectilinear case and deserves further investigation. The problem is solved in the present part III as an extension of part II. The robot executes a rectilinear walk on a local reference frame whose progression axis is always tangent, and its origin performs the involute of the path curve. The curve is defined by its curvature (osculating circle) and center of curvature (evolute) along the path. Radius of curvature and center can change continuously (in practice at every sampling time). For postural equilibrium, Center of Gravity and Zero Moment Point (COG/ZMP) follow the same preview reference proposed for rectilinear walk (c o g R e f x ( t ) , c o g ˙ R e f x ( t ), c o g R e f y ( t ) , c o g ˙ R e f y ( t )). The effect of the turn on the sagittal plane is negligible and is ignored, while on the frontal plane it is accounted for by an offset on COG reference to compensate for the centrifugal acceleration. The body trunk and local frame rotation, and the generation of the references on this moving frame of the free foot trajectory during the swing deserve attention.
Highlights
This part III extends the results of the previous part II of this paper, where the control of a biped robot in rectilinear walk was described
Our approach belongs to this second category of preview tracking, but unlike previous works, it is based on a running local reference frame with respect to which the robot maintains rectilinear walk, to rotate this frame and move its origin with respect to the world coordinates to follow an involute of the path curve during turns
In the local reference frame that accompanies the turn of the robot, COGx preview and COGy preview along l1 and l2 remain almost unchanged with respect to the rectilinear walk
Summary
This part III extends the results of the previous part II of this paper, where the control of a biped robot in rectilinear walk was described. Our approach belongs to this second category of preview tracking, but unlike previous works, it is based on a running local reference frame with respect to which the robot maintains rectilinear walk, to rotate this frame and move its origin with respect to the world coordinates to follow an involute of the path curve during turns. The trunk angle around the vertical axis is programmed to maintain continuously, during double and single stance, the frontal plane of the robot orthogonal to the walk path, and the swing foot angle follows the trunk using a feedback, similar to the one proposed by [10]. Different to the other approaches where the joint trajectories were computed with alternative techniques, or were not well documented, the rectilinear walk in a moving local frame defines a trajectory that can be, at each step, interpolated with simple polynomial functions in real time and corrected by feedback
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