Biped robots form a subclass of legged or walking robots. The study of mechanical legged motion has been motivated by its potential use as a means of locomotion in rough terrain, as well as its potential benefits to prothesis development and testing. This paper concentrates on issues related to the automatic control of biped robots. More precisely, its primary goal is to contribute a means to prove asymptotically-stable walking in planar, under actuated biped robot models. Since normal walking can be viewed as a periodic solution of the robot model, the method of Poincaré sections is the natural means to study asymptotic stability of a walking cycle. However, due to the complexity of the associated dynamic models, this approach has had limited success. The principal contribution of the present work is to show that the control strategy can be designed in a way that greatly simplifies the application of the method of Poincaré to a class of biped models, and, in fact, to reduce the stability assessment problem to the calculation of a continuous map from a subinterval of IR to itself. The mapping in question is directly computable from a simulation model. The stability analysis is based on a careful formulation of the robot model as a system with impulse effects and the extension of the method of Poincaré sections to this class of models.
This paper proposes new methodologies for the design of adaptive sliding mode control. The goal is to obtain a robust sliding mode adaptive gain control law with respect to uncertainties and perturbations without the knowledge of uncertainties/perturbations bound (only the boundness feature is known). The proposed approaches consist in having a dynamical adaptive control gain that establishes a sliding mode in finite time.. Gain dynamics ensures also that there is no over-estimation of the gain with respect to the real a priori unknown value of uncertainties. The efficacy of both proposed algorithms is confirmed on a tutorial example and while controlling an electropneumatic actuator.
A new predictive scheme is proposed for the control of Linear Time Invariant (LTI) systems with a constant and known delay in the input and unknown disturbances. It has been achieved to include disturbances effect in the prediction even though there are completely unknown. The Artstein reduction is then revisited thanks to the computation of this new prediction. An extensive comparison with the standard scheme is presented throughout the article. It is proved that the new scheme leads to feedback controllers that are able to reject perfectly constant disturbances. For time-varying ones, a better attenuation is achieved for a wide range of perturbations and for both linear and nonlinear controllers. A criterion is given to characterize this class of perturbations. Finally, some simulations illustrate the results.
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