Robust trajectory following of robots using computed torque structure with VSS.

*(English)*Zbl 0706.70033Summary: A control approach is proposed for robust accurate trajectory tracking of manipulators based on the computed torque technique and variable- structure systems (VSS) theory. The computed torque structure of the control scheme, most importantly, provides greater insight to the control of manipulators and serves as a unifying framework for control law development. Looking at the control structure from a computed torque perspective also enables the extension of the technique from joint space to direct end-effector control of both non-redundat and redundant robots in task or operational space. The technique, perhaps, may be further augmented to incorporate force control to achieve hybrid force/position control.

The use of sliding modes in the control scheme, in its idealized form, ensures accurate tracking while achieving insensitivity to parameter variations/uncertainties and bounded disturbances. In the development of the control laws, some useful properties of the robot dynamics, viz., positive definiteness of the inertia matrix, and its (dynamics structure) linear form with respect to its parameters, are exploited to make the control laws simple for real-time implementation and reflect the explicit inter-dependence of control nonlinearity and structured dynamic model uncertainty. The control algorithms obtained by various researchers for manipulator control using VSS theory may interpreted from the approach given, which thus to a certain extent unifies the VSS techniques suggested in the literature for robot control.

The use of sliding modes in the control scheme, in its idealized form, ensures accurate tracking while achieving insensitivity to parameter variations/uncertainties and bounded disturbances. In the development of the control laws, some useful properties of the robot dynamics, viz., positive definiteness of the inertia matrix, and its (dynamics structure) linear form with respect to its parameters, are exploited to make the control laws simple for real-time implementation and reflect the explicit inter-dependence of control nonlinearity and structured dynamic model uncertainty. The control algorithms obtained by various researchers for manipulator control using VSS theory may interpreted from the approach given, which thus to a certain extent unifies the VSS techniques suggested in the literature for robot control.

##### MSC:

70Q05 | Control of mechanical systems |

70B15 | Kinematics of mechanisms and robots |

93C85 | Automated systems (robots, etc.) in control theory |

##### Keywords:

control approach; robust accurate trajectory tracking; computed torque technique; variable-structure systems (VSS) theory; control law
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\textit{S. W. Wijesoma} and \textit{R. J. Richards}, Int. J. Control 52, No. 4, 935--962 (1990; Zbl 0706.70033)

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