This contribution shows a geometric optimal control procedure to solve the trajectory generation problem for the navigation (generic motion) of mechanical systems with revolute joints. The mechanical system is analyzed as a nonlinear Lagrangian system affected by dry friction at the joint level. Rayleigh’s dissipation function is used to model this dissipative effect of joint-level friction, and regarded as a potential. Rayleigh’s potential is an invariant scalar quantity from which friction forces derive and are represented by a smooth model that approaches the traditional Coulomb’s law in our proposal. For the optimal control procedure, an invariant cost function is formed with the motion equations and a Riemannian metric. The goal is to minimize the consumed energy per unit time of the system. Covariant control equations are obtained by applying Pontryagin’s principle, and time-integrated using a Finite Elements Method-based solver. The obtained solution is an optimal trajectory that is then applied to a mechanical system using a proportional–derivative plus feedforward controller to guarantee the trajectory tracking control problem. Simulations and experiments confirm that including joint-level friction forces at the modeling stage of the optimal control procedure increases performance, compared with scenarios where the friction is not taken into account, or when friction compensation is performed at the feedback level during motion control.

En este artículo se describe una mejora implementada al servomotor Dynamixel AX-12, un servomotor inteligente de bajo costo muy utilizado en el diseño y construcción de robots avanzados para entretenimiento e investigación. Se detalla la modificación de su software y hardware a fin de cambiar su protocolo de comunicación original por SPI y con esto lograr mayores velocidades de transmisión de datos entre servomotores del mismo tipo y sistemas de cómputo supervisores que operen en tiempo real. Adicionalmente, se le programa un controlador PD con prealimentación para regular tanto la velocidad como la posición angular de su eje de carga, con un periodo de muestreo de 1 [ms] (10 veces mayor respecto a lo alcanzado con el servomotor original). Finalmente se describen las conclusiones obtenidas respecto al comportamiento satisfactorio tanto de lo teórico como de lo experimental.

This article presents an experimental platform for testing friction models used by control strategies on a one-degree-of-freedom mechanical motion control system. This platform aims to carry out experiments to estimate dry friction parameters and related motion control strategies. The presented device can be built using low-cost components available in most laboratories. The platform enables both a correct friction parameters estimation and the experimental validation of related motion control strategies. The proposed platform can be applied to the validation of a wide spectrum of parameter identification and motion control procedures. Experimental results illustrate the usability of the proposed device for research purposes. However, the platform could be used as an educational device to illustrate the performance of specific friction models with various control strategies.