Equation of Motion of the Nonlinear Robotic Systems with Constraints

This paper presents a simple methodology for obtaining the entire set of continuous controllers that cause a nonlinear dynamical system to exactly track a given trajectory. The trajectory is provided as a set of algebraic differential equations that may or may not be explicitly dependent on time. The method provided is inspired by results from analytical dynamics and the close connection between nonlinear control and analytical dynamics is explored. The results provided in this paper here yield new and explicit methods for the control of highly nonlinear systems. The paper is based on previous work of the authors.