Alejandro Rodriguez-Angeles, Marco A. Arteaga-Pérez, Rogelio de J. Portillo-Vélez, e e and Carlos A. Cruz-Villar


Teleoperation, master-slave systems, position–force tracking control,transparency, force reflecting


This work develops a bilateral master–slave control approach based on virtual surfaces for the master and direct force reflecting from the slave robot. Real and virtual surfaces are modeled by holonomic constraints, allowing joint orthogonal decomposition into force and position spaces to be considered. A stability analysis is provided and convergence properties for position and force errors are drawn, yielding transparency of the bilateral master–slave system. The reaction force between the real surface and the slave robot is measured by a force sensor and this signal is sent for force reflecting to the master robot. On the master robot, a holonomic constraint generates a virtual surface. Between the operator and the virtual surface, a virtual force arises and it is obtained via a Lagrange multiplier. The virtual force is regulated to converge to the measured reaction force at the slave robot. Thus, the operator feels the virtual force as a reaction force, and convergence from the virtual to the slave reaction force makes the user feels the environment reaction force. Inclusion of the virtual force allows decoupling of the operator and the real reflected slave reaction force, which helps to improve the force bandwidth and stability of the bilateral system, mainly at transient stage. The virtual surface and the virtual reaction force allow the integration of a force sensor at the master robot to determine the desired force exerted by the operator by direct measurement. This approach greatly improves transparency ∗ Centro de Investigaci´on y de Estudios Avanzados del I.P.N. Avenida I.P.N., 2508, Departamento de Ingenier´ıa El´ectrica, Secci´on de Mecatr´onica, Colonia San Pedro Zacatenco, M´exico, D.F., M´exico; e-mail:, A. Rodr´ıguez–´Angeles is currently on Sabbatical leave at Dynamics and Control Group, Department of Mechanical Engineering, Eindhoven Univer- sity of Technology. Eindhoven, The Netherlands; e-mail: ∗∗ Departamento de Control y Rob´otica, Divisi´on de Inge- nier´ıa El´ectrica de la Facultad de Ingenier´ıa, Universidad Nacional Aut´onoma de M´exico, M´exico, D.F., M´exico; e-mail: ∗∗∗ Facultad de Ingenier´ıa, Universidad Aut´onoma del Carmen, Avenida Concordia, Colonia Aviaci´on, Cd. del Carmen, Campeche, M´exico; e-mail: Recommended by Prof. J. Gu and results in a haptic system with software–hardware in the loop. The proposed scheme is tested on a real platform, showing good agreement between theoretical and experimental results.

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