A port-Hamiltonian approach to the control of nonholonomic systems
For control engineers working on nonholonomic systems, this work provides a robust stabilization method within the port-Hamiltonian framework, though it is an incremental extension of existing chained-form approaches.
The paper presents a discontinuous control law for nonholonomic systems modeled in the port-Hamiltonian framework, achieving asymptotic stabilization to the origin. The method is robust to damping and inertia, demonstrated numerically on a car-like vehicle.
In this paper a method of controlling nonholonomic systems within the port-Hamiltonian (pH) framework is presented. It is well known that nonholonomic systems can be represented as pH systems without Lagrange multipliers by considering a reduced momentum space. Here, we revisit the modelling of these systems for the purpose of identifying the role that physical damping plays. Using this representation, a geometric structure generalising the well known chained form is identified as \textit{chained structure}. A discontinuous control law is then proposed for pH systems with chained structure such that the configuration of the system asymptotically approaches the origin. The proposed control law is robust against the damping and inertial of the open-loop system. The results are then demonstrated numerically on a car-like vehicle.