A passivity approach to controller-observer design for robots

Passivity-based control methods for robots, which achieve the control objective by reshaping the robot system's natural energy via state feedback, have, from a practical point of view, some very attractive properties. However, the poor quality of velocity measurements may significantly deteriorate the control performance of these methods. In this paper the authors propose a design strategy that utilizes the passivity concept in order to develop combined controller-observer systems for robot motion control using position measurements only. To this end, first a desired energy function for the closed-loop system is introduced, and next the controller-observer combination is constructed such that the closed-loop system matches this energy function, whereas damping is included in the controller- observer system to assure asymptotic stability of the closed-loop system. A key point in this design strategy is a fine tuning of the controller and observer structure to each other, which provides solutions to the output-feedback robot control problem that are conceptually simple and easily implementable in industrial robot applications. Experimental tests on a two-DOF manipulator system illustrate that the proposed controller-observer systems enable the achievement of higher performance levels compared to the frequently used practice of numerical position differentiation for obtaining a velocity estimat

Nonlinear Receding-Horizon Control of Rigid Link Robot Manipulators

The approximate nonlinear receding-horizon control law is used to treat the trajectory tracking control problem of rigid link robot manipulators. The derived nonlinear predictive law uses a quadratic performance index of the predicted tracking error and the predicted control effort. A key feature of this control law is that, for their implementation, there is no need to perform an online optimization, and asymptotic tracking of smooth reference trajectories is guaranteed. It is shown that this controller achieves the positions tracking objectives via link position measurements. The stability convergence of the output tracking error to the origin is proved. To enhance the robustness of the closed loop system with respect to payload uncertainties and viscous friction, an integral action is introduced in the loop. A nonlinear observer is used to estimate velocity. Simulation results for a two-link rigid robot are performed to validate the performance of the proposed controller. Keywords: receding-horizon control, nonlinear observer, robot manipulators, integral action, robustness

A family of asymptotically stable control laws for flexible robots based on a passivity approach

A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility

Discrete-time adaptive control of robot manipulators

A discrete-time model reference adaptive control scheme is developed for trajectory tracking of robot manipulators. Hyperstability theory is utilized to derive the adaptation laws for the controller gain matrices. It is shown that asymptotic trajectory tracking is achieved despite gross robot parameter variation and uncertainties. The method offers considerable design flexibility and enables the designer to improve the performance of the control system by adjusting free design parameters. The discrete-time adaptation algorithm is extremely simple and is therefore suitable for real-time implementation

Global regulation of robots using only position measurements

In this note we propose a simple solution to the regulation problem of rigid robots based on the availability of only joint position measurements. The controller consists of two parts: (1) a gravitation compensation, (2) a linear dynamic first-order compensator. The gravitation compensation part can be chosen to be a function of either the actual joint position or the desired joint position. Both possibilities are aproved to yield global asymptotic stability. Performance issues of the controller are illustrated in a simulation study of a two degrees-of-freedom robot manipulator