Tackling mismatched uncertainty in robust constraintfollowing control of underactuated systems Abstract   The mismatched uncertainty makes the control for underactuated systems an intractable problem in the control field. This paper targets this problem based on constraintfollowing. The uncertainty is (possibly fast) timevarying and bounded. The control goal is to drive underactuated systems to follow prescribed constraints, which may be holonomic or nonholonomic, linear or nonlinear with respect to the velocity. The control is designed in two steps. First, the nominal control without addressing uncertainties and initial condition deviations is investigated. Second, we meticulously decompose uncertainty into matched and mismatched portions. This decomposition makes the mismatched uncertainty xe2x80x9cdisappearxe2x80x9d in the stability analysis. Consequently, we are able to design a class of robust constraintfollowing controls free from mismatched uncertainty and only based on matched uncertainty. By the Lyapunov approach, we show that the proposed robust controls guarantee uniform boundedness and uniform ultimate boundedness for underactuated systems. Simulation results on a mobile robot are given for demonstrations.

Periodic Trajectory Planning and Robust Output Zeroing Control for Underactuated Bipedal Robots with Predicted Disturbances For underactuated bipedal robots, it is important to compensate disturbances which affects the zero dynamics to realize a stable locomotion when we use output zeroing controllers. In order to deal with such disturbances, this paper presents a framework of a periodic trajectory planning and a robust output zeroing controller using a disturbance model learned by Gaussian process regression (GPR). In particular, we propose a control method considering the modeling uncertainty of the disturbance model by using a variance information of GPR model. We show the effectiveness of the proposed method through a numerical simulation of walking control of an underactuated robot model affected by an external force.