Feedback linearization is a viable nonlinear control technique for solving trajectory tracking problems in robots with (and without) elastic joints. However, the additional presence of dissipative effects due to joint viscosity destroys full state feedback linearizability. For robots with visco-elastic joints, the use of a static state feedback can achieve at most input-output linearization and decoupling, since an internal nonlinear dynamics is left in the closed-loop system. Although the stability properties of this unobservable dynamics still guarantee perfect output tracking in nominal conditions, control design based on static feedback becomes ill-conditioned as joint viscosity decreases. Instead, resorting to a nonlinear dynamic state feedback leads to the same closed-loop properties, but with a regularized control effort for any level of joint viscosity and elasticity. Static and dynamic nonlinear feedback control designs are presented for a reduced and a complete dynamic model of visco-elastic joint robots. A numerical comparison on a simple case study illustrates the benefits of the dynamic input-output linearization approach.

The classical dynamic scaling property of robot trajectories is analyzed in the case of presence of elastic transmissions. We present a technique for recovering the fastest motion under torque constraints, when uniform time scaling is used along a given path. The scaling algorithm is based on the solution of a complete quartic polynomial equation, which reduces to a biquadratic one in the absence of viscous friction. Consequences on the organization of inverse dynamics computation are pointed out. Numerical results are reported for a planar 2R arm, illustrating the differences that arise with respect to the fully rigid case.