Tracking Control of Fully-actuated port-Hamiltonian Mechanical Systems via Sliding Manifolds and Contraction Analysis

In this paper, we propose a novel trajectory tracking controller for fully-actuated mechanical port-Hamiltonian (pH) systems, which is based on recent advances in contraction- based control theory. Our proposed controller renders a desired sliding manifold (where the reference trajectory lies) attractive by making the corresponding pH error system partially contracting. Finally, we present numerical simulation results where a SCARA robot is commanded by our proposed tracking control law

A family of virtual contraction based controllers for tracking of flexible-joints port-Hamiltonian robots:Theory and experiments

In this work, we present a constructive method to design a family of virtual contraction based controllers that solve the standard trajectory tracking problem of flexible-joint robots in the port-Hamiltonian framework. The proposed design method, called virtual contraction based control, combines the concepts of virtual control systems and contraction analysis. It is shown that under potential energy matching conditions, the closed-loop virtual system is contractive and exponential convergence to a predefined trajectory is guaranteed. Moreover, the closed-loop virtual system exhibits properties such as structure preservation, differential passivity, and the existence of (incrementally) passive maps. The method is later applied to a planar RR robot, and two nonlinear tracking control schemes in the developed controllers family are designed using different contraction analysis approaches. Experiments confirm the theoretical results for each controller

Virtual contractivity-based control of fully-actuated mechanical systems in the port-Hamiltonian framework

We present a trajectory tracking control design method for a class of mechanical systems in the port-Hamiltonian framework. The proposed solution is based on the virtual contractivity-based control (v-CBC) method, which employs the notions of virtual systems and of contractivity. This approach leads to a family of asymptotic tracking controllers that are not limited to those that preserve the pH structure of the closed-loop system nor require an intermediate change of coordinates. Nevertheless, structure preservation and other properties (e.g., passivity) are possible under sufficient conditions. The performance of the proposed v-CBC scheme is experimentally evaluated on a planar robot of two degrees of freedom (DoF)