The Use of Kane's Dynamical Equations in Robotics

Abstract

Extensive experience has shown that the use of general- purpose, multibody-dynamics computer programs for the numerical formulation and solution of equations of motion of robotic devices leads to slow evaluation of actuator forces and torques and slow simulation of robot motions. In this paper, it is shown how improvements in computational efficiency can be effected by using Kane's dynamical equations to formulate explicit equations of motion. To these ends, a detailed analysis of the Stanford Arm is presented in such a way that each step in the analysis serves as an illustrative example for a general method of attack on problems of robot dynamics. Simulation results are reported and are used as a basis for discussing questions of computational efficiency.

Evolution of the DeNOC-based dynamic modelling for multibody systems

“…Hence,w n = w n . The effect of gravity can also be taken into account by providing negative acceleration due to gravity, g, to the twist-rate of the first link as an additional term (Kane and Levinson, 1983), i.e.,…”

“…Kane's formulation (Kane and Levinson, 1983), which is same as the Lagrange's form of D'Alembert's principle, has also been used by many researchers for the development of equations of motion. It is found to be more beneficial than other formulations when used for systems with nonholonomic constraints.…”

Non-Adaptive Sliding Mode Controllers in Terms of Inertial Quasi-Velocities

“…Note however, that the controls algorithms can be realized using quantities arising from the spatial operators which decrease their computational complexity Jain & Rodriguez (1995). Also Kane's equations are computationally effective Kane & Levinson (1983). Thus, the algorithms seem a useful tool for simulation of serial rigid manipulators.…”

“…The Loduha and Ravani offer the generalized velocity components (GVC) which can be related to the modified Kane's equations given e.g. in Kane & Levinson (1983). Finally, also the normalized generalized velocity components (NGVC) are considered in references Herman (2005b;2006).…”

Parallelism in Manipulator Dynamics

“…The notation is based on that used by Hollerbach (1980), Luh, Walker, and Paul ( 1980a), and Lathrop (1983) Kane and Levinson 1983;Lathrop 1983).…”