A Nonlinear Optimal Control Approach for Multi-DOF Brachiation Robots

This paper proposes a nonlinear optimal control approach for mulitple degrees of freedom (DOF) brachiation robots, which are often used in inspection and maintenance tasks of the electric power grid. Because of the nonlinear and multivariable structure of the related state-space model, as well as because of underactuation, the control problem of these robots is nontrivial. The dynamic model of the brachiation robots undergoes first approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the Jacobian matrices of the brachiation robots’ state-space model. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the brachiation robots, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The global stability properties of the control scheme are proven through Lyapunov analysis. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the brachiation robots, under moderate variations of the control inputs.

A nonlinear optimal control approach for underactuated power-line inspection robots

The article proposes a nonlinear optimal (H-infinity) control approach for a type of underactuated power-line inspection robots. To implement this control scheme, the state-space model of the power-line inspection robots undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. To select the feedback gains of the controller an algebraic Riccati equation is solved at each time step of the control method. The global stability properties of the control loop are proven through Lyapunov analysis. The significance of the article’s results is outlined in the following: (i) the proposed control method is suitable for treating underactuated robotic systems and in general nonlinear dynamical systems with control inputs gain matrices which are in a nonquadratic form, (ii) by achieving stabilization of the power-line inspection robots in underactuation conditions the proposed control method ensures the reliable functioning of these robotic systems in the case of actuators’ failures or enables the complete removal of certain actuators and the reduction of the weight of these robotic systems, (iii) the proposed control method offers a solution to the nonlinear optimal control problem which is of proven global stability while also remaining computationally tractable, (iv) the proposed nonlinear optimal control method retains the advantages of linear optimal control that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs, and (v) by minimizing the amount of energy that is dispersed by the actuators of the power-line inspection robots the proposed control method improves the autonomy and operational capacity of such robotic systems.