Simplification of manipulator dynamic model for nonlinear decoupled control

The authors develop simplified manipulator dynamic models which satisfy the desired steady-state error specification in the joint-variable space or the Cartesian space under a nonlinear decoupled controller. The formulas which relate the tracking errors of joint variables in the joint-variable space or the manipulator hand in the Cartesian space to the dynamic modeling errors are derived and used to obtain the maximum error tolerance for each dynamic coefficient of the equations of motion. Then each simplified dynamic coefficient of the equations of motion can be expressed as a linear combination of the product terms of sinusoidal and polynomial basis functions. To illustrate the approach, a computer simulation was carried out to obtain two simplified dynamic models of a Stanford robot arm which satisfy the above condition