Optimization of the Internal Dynamics of Underactuated Robots

A robot is underactuated if it possesses less control inputs than degrees of freedom, e.g. due to passive joints. The analysis of the mechanical design of these kinds of underactuated robots often shows that they are non-minimum phase, i.e. they have an internal dynamic which is not asymptotically stable. Therefore, feedback linearization is not possible, and output trajectory tracking becomes a very challenging task. It is shown that through an optimization procedure the mechanical design of an underactuated robot can be altered in such a way that the internal dynamics becomes stable. Thus feedback linearization of the underactuated robot becomes possible. In the optimization procedure, the design parameters are additional masses which are added to defined locations at different un-actuated links of the robot. The optimization criteria is two-stage and firstly requires that all eigenvalues of the linearized zero-dynamics are in the left half-plane and secondly that initial errors in the zero-dynamics decay rapidly. Due to the two-stage criteria computation the optimization problem is discontinuous. Also there might be many local minima. Therefore a particle swarm optimization procedure is used. The efficiency of this optimization approach is demonstrated by simulation of an underactuated robot. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)