Abstract
A robot designed to mimic a human becomes kinematically redundant and its total degrees of freedom becomes larger than the number of physical variables required for describing a given task. Kinematic redundancy may contribute to enhancement of dexterity and versatility but it incurs a problem of ill-posedness of inverse kinematics from the task space to the joint space. This ill-posedness was originally found by Bernstein, who tried to unveil the secret of the central nervous system and how nicely it coordinates a skeletomotor system with many DOFs interacting in complex ways. In the history of robotics research, such ill-posedness has not yet been resolved directly but circumvented by introducing an artificial performance index and determining uniquely an inverse kinematics solution by minimization. This paper tackles such Bernstein's problem and proposes a new method for resolving the ill-posedness in a natural way without invoking any artificial index. First, given a curve on a horizontal plane for a redundant robot arm whose endpoint is imposed to trace the curve, the existence of a unique ideal joint trajectory is proved. Second, such a uniquely determined motion can be acquired eventually as a joint control signal through iterative learning without reinforcement or reward.
Highlights
Almost a quarter century ago, “robotics” was defined by Professor Brady at the first International Conference of Robotics Research [1] as “the intelligent connection of perception to action.” After a great deal of researches on developments of industrial robots and their applications, a variety of research projects on “humanoid” have attracted many roboticists during the past decade and nowadays robots that can walk with a bipedal mode are not peculiar
Kinematic redundancy may contribute to enhancement of dexterity and versatility but it incurs a problem of ill-posedness of inverse kinematics from the task space to the joint space
This ill-posedness was originally found by Bernstein, who tried to unveil the secret of the central nervous system and how nicely it coordinates a skeletomotor system with many DOFs interacting in complex ways
Summary
Almost a quarter century ago, “robotics” was defined by Professor Brady at the first International Conference of Robotics Research [1] as “the intelligent connection of perception to action.” After a great deal of researches on developments of industrial robots and their applications, a variety of research projects on “humanoid” have attracted many roboticists during the past decade and nowadays robots that can walk with a bipedal mode are not peculiar. More than a half century ago preceding the birth of “humanoid,” Bernstein [2, 3] noted that dexterity of human body movements resides in involvement of surplus degrees of freedom of limb joints but this incurs the ill-posedness of inverse kinematics This was introduced to the robotics community through the famous textbook [4] in page 303 in such a statement as “The study of human biological motor control mechanisms led the Russian psychologist Bernstein to question how the brain could control a system with so many different degrees of freedom interacting in such a complex fashion. (a) What can we infer about the code that the brain uses to communicate with the periphery, and what does that tell us about how the computation is organized?, (b) If the brain knew just what movements it wanted the body to make, could it figure out what to tell the muscles in order to make
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