Simulation approach to the inverse dynamics of underactuated systems

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A new simulation approach to the inverse dynamics of underactuated mechanical systems is proposed. Typical sample applications are cranes and robot manipulators. The simulation approach is based on the numerical solution of servo problems. In the case of cranes servo constraints are used to prescribe the trajectory of the load. The solution of the servo problem determines the actuating forces that are required to realize the prescribed motion of the load. In addition to the servo constraints the servo problem comprises the equations of motion pertaining to the mechanical system at hand. Consequently, the governing equations assume the form of differential-algebraic equations (DAEs). The DAEs typically have high index and are thus notoriously difficult to solve. A new index reduction method is proposed to facilitate the stable numerical solution of the servo problem. Moreover, a new continuous Galerkin method in space and time is developed which will be especially beneficial for the inverse dynamics of robots with flexible components.