Adaptive control of underactuated robots with unmodeled dynamics

• An adaptive control formulation for underactuated robotic systems with unmodeled dynamics is proposed.
• The design allows for fast estimation while guaranteeing bounded deviation from a nonadaptive reference system.
• The proposed formulation is independent of detailed information about the system model.
• The proof of stability is established by the analysis based on input–output maps.
• The system’s robustness to measurement noise and time delay is demonstrated.

This paper develops an adaptive controller for underactuated robotic systems with unmodeled dynamics. The control scheme is motivated by the applications of manipulators operating on dynamic platforms. The design decouples the system’s adaptation and control loops to allow for fast estimation rates, while guaranteeing bounded deviation from a nonadaptive reference system. The proposed formulation is independent of detailed information about the system model. The control scheme is tested in different trajectory-tracking scenarios: (i) a manipulator installed on a ship operating in a high-sea state with uncertain environmental disturbances and (ii) a mobile manipulator moving across a rough terrain of unknown geometry. The simulation results illustrate the tracking performance of the proposed control algorithm, its ability to deal with unmodeled dynamics, and its robustness to measurement noise and time delay, while maintaining smooth control signals.