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History of Robotics Research and Development of Japan2005Integration, Intelligence, etc.Natural resolution of ill-posedness of inverse kinematics for redundant robots

Suguru ArimotoRitsumeikan University
Masahiro SekimotoRitsumeikan University (currently University of Toyama)
Hiroe HashiguchiRitsumeikan University (currently Daido University)
Ryuta OzawaRitsumeikan University
A robot designed to mimic a human becomes kinematically redundant, i.e. its total degrees of freedom becomes larger than the number of physical variables required for description of a given task. Kinematic redundancy in control of this type of robot may contribute to enhancement of dexterity and versatility, but incurs a problem of ill-posedness of inverse kinematics from the task-description space to the robot joint space. Such ill-posedness of inverse kinematics was originally found by A. N. Bernstein as the "degrees-of-freedom problem" in physiology. However, in the history of robotics research, such ill-posedness of inverse kinematics has not yet been tackled directly, but circumvented by introducing an artificial performance index and determining uniquely an inverse kinematics solution by minimizing it. This research aimed at challenging one of Bernstein's problems and proposed a new method for resolving such an ill-posedness problem in a natural way and in a dynamic sense without invoking any artificial performance index. Instead, a novel concept named "stability on a manifold" was introduced and it was shown that there exists a sensory feedback signal from the task space to the joint space such that it enables the solution of overall closed-loop dynamics to converge naturally and coordinately to a lower dimensional manifold describing a set of joint states fulfilling a given motion task. This result is extended by using the concept of "transferability to a submanifold," and it was proven that a task-space feedback control with the Jaconbian transpose allows it to accomplish redundant multi-joint reaching without determining any joint space trajectory. 21th RSJ Best Paper Award in 2007.

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Redundant multi-joint reaching

Correspondence papers

S. Arimoto, M. Sekimoto, H. Hashiguchi, and R. Ozawa：Natural resolution of ill-posedness of inverse kinematics for redundant robots: A challenge to Bernstein's degrees-of-freedom problem

Advanced Robotics, Vol. 19, No. 4, pp. 401-434, 2005.

Related papers

[1] M. Takegaki and S. Arimoto: "A new feedback method for dynamic control of manipulators," Trans. of the ASME J. of Dynamic Systems, Measurement and Control, Vol. 103, No. 2, pp. 119-25, 1981.

[2] S. Arimoto, K. Tahara, J.-H. Bae, and M. Yoshida: "A stability theory on a manifold: concurrent realization of grasp and orientation control of an object by a pair of robot fingers," Robotica, Vol. 21, No. 2, pp. 163-178, 2003.

[3] S. Arimoto, M. Sekimoto, and R. Ozawa: "A challenge to Bernstein's degrees-of-freedom problem in both cases of human and robotic multi-joint movements," IEICE Transactions on Fundamentals of Electronics, Communications, and Computer Sciences, Vol.E88-A, No.10, pp.2484-2495, 2005.

[4] S. Arimoto, H. Hashiguchi, M. Sekimoto, and R. Ozawa: "Generation of natural motions for redundant multi-joint systems: A differential-geometric approach based upon the principle of least actions," J. of Robotic Systems, Vol.22, No.11, pp.583-605, 2005.

[5] M. Sekimoto and S. Arimoto: "A natural redundancy-resolution for 3-D multi-joint reaching under the gravity effect," J. of Robotic Systems, Vol.22, No.11, pp.607-623, 2005.

[6] S. Arimoto and M. Sekimoto: "Natural resolution of ill-posed inverse kinematics for redundant robots: A challenge to Bernstein's Degrees-of-freedom problem," J. of Robotics and Mechatronics, Vol.18, No.5, pp.651-660, 2006.

[7] M. Sekimoto and S. Arimoto: "Experimental study on control method for robot arms with redundant joints based upon virtual spring-damper hypothesis," J. of the Robotics Society of Japan, Vol.25, No.5, pp.785-791, 2007. (in Japanese)

[8] S. Arimoto, M. Yoshida, M. Sekimoto, and K. Tahara: "A Riemannian-geometry approach for control of robotic systems under constraints," SICE J. of Control, Measurement, and System Integration, Vol.2, No.2, pp.107-116, 2009.

[9] S. Arimoto, and M. Sekimoto: "An optimal regulator for stabilization of multi-joint reaching movements under DOF-redundancy: A challenge to the Bernstein problem from a control-theoretic viewpoint," Proceedings of the Institution of Mechanical Engineers, Part I: J. of Systems and Control Engineering, Vol.225, No.6, pp.779-789, 2011.

[10] S. Arimoto: "Optimal linear quadratic regulators for control of nonlinear mechanical systems with redundant degrees-of-freedom," SICE J. of Control, Measurement, and System Integration, Vol. 4, No. 4, pp. 289–294, 2011.

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