TY - GEN
T1 - A new method for determining joint constraint forces and moments during optimal dynamic motion of redundant manipulators
AU - Kim, Joo H.
AU - Yang, Jingzhou
AU - Abdel-Malek, Karim
PY - 2008
Y1 - 2008
N2 - The kinematic representations of general open-loop chains in many robotic applications are based on the Denavit-Hartenberg (DH) notation. However, when the DH representation is used for kinematic modeling, the relative joint constraints cannot be described explicitly using the common formulation methods. In this paper, we propose a new formulation of solving a system of differential-algebraic equations (DAEs) where the method of Lagrange multipliers is incorporated into the optimization problem for optimal motion planning of redundant systems. In particular, a set of fictitious joints is modeled to solve for the joint constraint forces and moments, as well as the optimal dynamic motion and the required actuator torques, of redundant manipulators described in DH representation. The proposed method is formulated within the framework of our earlier study on the generation of load-effective optimal dynamic motions of redundant manipulators that guarantee successful execution of given tasks, in which the Lagrangian dynamics for general external loads are incorporated. Some example tasks of a simple planar manipulator and a high-degree-of-freedom digital human model are illustrated, and the results show accurate calculation of joint constraint loads without altering the original planned motion. The proposed optimization formulation is equivalent to solving DAEs without integration.
AB - The kinematic representations of general open-loop chains in many robotic applications are based on the Denavit-Hartenberg (DH) notation. However, when the DH representation is used for kinematic modeling, the relative joint constraints cannot be described explicitly using the common formulation methods. In this paper, we propose a new formulation of solving a system of differential-algebraic equations (DAEs) where the method of Lagrange multipliers is incorporated into the optimization problem for optimal motion planning of redundant systems. In particular, a set of fictitious joints is modeled to solve for the joint constraint forces and moments, as well as the optimal dynamic motion and the required actuator torques, of redundant manipulators described in DH representation. The proposed method is formulated within the framework of our earlier study on the generation of load-effective optimal dynamic motions of redundant manipulators that guarantee successful execution of given tasks, in which the Lagrangian dynamics for general external loads are incorporated. Some example tasks of a simple planar manipulator and a high-degree-of-freedom digital human model are illustrated, and the results show accurate calculation of joint constraint loads without altering the original planned motion. The proposed optimization formulation is equivalent to solving DAEs without integration.
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U2 - 10.1115/DETC2007-35677
DO - 10.1115/DETC2007-35677
M3 - Conference contribution
AN - SCOPUS:44949216720
SN - 0791848027
SN - 9780791848029
SN - 079184806X
SN - 9780791848067
T3 - 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
SP - 161
EP - 172
BT - 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
T2 - 6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007
Y2 - 4 September 2007 through 7 September 2007
ER -