Natural resolution of ill-posedness of inverse kinematics for redundant robots: a challenge to Bernstein's degrees-of-freedom problem

Task-Space Iterative Learning for Redundant Robotic Systems: Existence of a Task-Space Control and Convergence of Learning

“…This reason is discussed in detail in the previous papers [6], [7]. Now, it is possible to state the main result of the paper: Proposition 1 For a given twice continuously differentiable endpoint trajectory x d (t) satisfying Assumption 1 or eq.…”

“…The reason is that redundancy in DOFs of objective dynamics may incur illposedness of inverse kinematics and make the control problems more sophisticated. It was very recent that even in the case of redundant arms a task space PD feedback for multi-joint reaching produces satisfactory skilled motions without calculating the pseudo-inverse of a Jacobian matrix or introduce any cost function to determine the inverse kinematics uniquely [6]- [8]. In the problem of Point-to-Point (PTP) reaching, there is no need of planning a trajectory in the task space in advance.…”

Iterative Learning without Reinforcement or Reward for Multijoint Movements: A Revisit of Bernstein's DOF Problem on Dexterity

“…However, in the physiological literature, there is a dearth of papers that attempted to directly deal with reaching movements with redundant joints, though the importance of Bernstein's DOF problem [2] has been widely known among physiologists. Differently from the traditional approaches, a simpler control method for multijoint reaching movements was proposed very recently in our previous papers [29][30][31] and shown to be effective in both cases of human and robotic arms with redundant DOFs. In those papers, only planar motions confined to a horizontal plane are treated and therefore the control signal is free from gravity with a simple form (see Figure 3)…”

“…However, all these treatments are restricted to planar motions as well as in most of the previous papers on multijoint reaching movements. In addition, another disadvantage is that choice of damping factors recommended in [29] is not fit to the scale of coefficients of viscosity of human muscles [34,35]. To reduce damping factors in general, another control method based upon "Virtual Spring-Damper Hypothesis" was suggested in [31], which in the case of planar motions without affection of the gravity is expressed by the form…”

The new robotics—towards human‐centered machines

“…Robotics theory has developed methods of hierarchical task prioritization (Nakamura, 1991;Khatib et al, 2004;Sentis and Khatib, 2004;Arimoto et al, 2005;Peters et al, 2005b) that, in theory, are quite appealing and capable. In recent work, Sentis and Khatib (Khatib et al, 2002;Khatib et al, 2004;Sentis and Khatib, 2004) demonstrated that rather natural looking behaviors could be generated with appropriate taskspace controllers and hierarchies.…”