In this paper, a sliding mode control using a control point concept is proposed for an under-actuated quadrotor. The proposed controller controls the position of the control point, a displaced point from the quadrotor’s geometric center, and the yaw angle. This method solves singularity issues in control matrix inversion and enables the utilization of the multi-input multi-output equation to derive the control inputs. The sliding surface is designed to control four outputs while stabilizing roll and pitch angles. Simulation and experimental results show the effectiveness and robustness of the proposed controller in the tracking of a trajectory under parametric uncertainties.

This paper presents a control law for the tracking of a cyclic reference path by an under-actuated biped robot. The robot studied is a five-link planar biped. The degree of under-actuation is one during the single support phase. The control law is defined in such a way that only the geometric evolution of the biped configuration is controlled, but not the temporal evolution. To achieve this objective, we consider a parametrized control. When a joint path is given, a five degree of freedom biped in single support becomes similar to a one degree of freedom inverted pendulum. The temporal evolution during the geometric tracking is completely defined and can be analyzed through the study of a model with one degree of freedom. Simple analytical conditions, which guarantee the existence of a cyclic motion and the convergence towards this motion, are deduced. These conditions are defined on the reference trajectory path. The analytical considerations are illustrated with some simulation results.