Input–output partial feedback linearisation is experimentally implemented on a non-smooth nonlinear system without the necessity of a conventional system matrix model for the first time. The experimental rig consists of three lumped masses connected and supported by springs with low damping. The input and output are at the first degree of freedom with a non-smooth clearance-type nonlinearity at the third degree of freedom. Feedback linearisation has the effect of separating the system into two parts: one linear and controllable and the other nonlinear and uncontrollable. When control is applied to the former, the latter must be shown to be stable if the complete system is to be stable with the desired dynamic behaviour.

In the biped robotics domain, head oscillations may be extremely harmful, especially if the robot is teleoperated, since vibrations strongly reduce the operator’s spatial awareness. In particular, undesired head oscillations occur in under-actuated robots, where springs and passive mechanisms are used to achieve a human-like motion. This paper proposes an approach to reduce the vibrations of a biped robot’s head; the proposed solution does not affect the dynamic locomotion properties, on which specific control logic could have been already tuned. The approach is tested on Rollo, a flexible-biped-wheeled robot, whose head vibrates throughout the robot locomotion. The two requirements, i.e., head vibration reduction and unchanged Rollo locomotion properties, are traduced in constraints to the robot possible modifications. Based on a 1D finite element model of the robot, tuned on experimental modal analysis, the undesired vibration causes are detected, and a solution for their reduction is proposed. Rollo’s head vibration amplitude is attenuated using a tuned vibration absorber, which achieves impressive performance in the robot. An archetype of the proposed vibration absorber is tailored designed on Rollo, without invasive changes to the robot structure. The proposed approach solves a significant problem in the biped robotic research community. The approach used to reduce the Rollo head oscillations may be utilized in other biped robot machines with or without flexible legs.