Abstract: The problem is to create a hybrid periodic motion, reminiscent of walking, for a model of an underactuated biped robot. We show how to construct a transverse linearization analytically and how to use it for stability analysis and for design of an exponentially orbitally stabilizing controller. In doing so, we extend a technique recently developed for continuous-time controlled mechani...

In this paper, two nonlinear H∞ control techniques are used to solve the position control problem of underactuated cooperative manipulators. The first technique consists in representing the nonlinear system in a quasi-linear parameter varying form and the solution is given in terms of linear matrix inequalities. The second technique gives an explicit solution to the cooperative manipulators H∞ ...

The trajectory generation problem for fault-tolerant robot manipulators is considered. A new technique which extends the Inverse Kinematics optimization approach to the case of robots with actuator faults is proposed. A bound on the second-order non-integrable constraints resulting from underactuation is assumed, and the trajectory generation problem is formulated as a nonlinear time-varying st...

The primary concern of the work is robust control of hybrid mechanical systems under unilateral constraints with underactuation degree one. Nonlinear H∞ output feedback synthesis is developed in the hybrid setting, covering collision phenomena. Sufficient conditions are presented to ensure internal asymptotic stability while also attenuating external disturbances and plant uncertainties. The de...

The operational space formulation (Khatib, 1987), applied to rigid-body manipulators, describes how to decouple task-space and null-space dynamics, and write control equations that correspond only to forces at the end-effector or, alternatively, only to motion within the null-space. We would like to apply this useful theory to modern humanoids and other legged systems, for manipulation or simil...

In this paper a constructive approach to the stabilization of a desired equilibrium for a class of underactuated mechanical systems via the Immersion & Invariance methodology (I&I) is proposed. The design procedure shows that cases of mechanical systems with underactuation degree greater than one are included. This work generalizes the results recently reported by the authors, where an approach...

The primary concern of the work is robust control of hybrid mechanical systems under unilateral constraints with underactuation degree one. Nonlinear H∞ output feedback synthesis is developed in the hybrid setting, covering collision phenomena. Sufficient conditions are presented to ensure internal asymptotic stability while also attenuating external disturbances and plant uncertainties. The de...

We consider in this paper the problem of (asymptotic) stabilization, via position feedback, of mechanical systems with underactuation degree one. A full state–feedback design is first derived applying Interconnection and Damping Assignment PassivityBased Control to which an Immersion and Invariance speed estimator is then added. The technique is applied to obtain an (almost) globally stabilizin...