Recently, through the use of parameterized fuzzy approximators, various adaptive fuzzy control schemes have been developed to deal with nonlinear systems whose dynamics are poorly understood. An important class of parameterized fuzzy approximators is constructed using radial basis function (RBF) as a membership function. However, some tuneable parameters in RBF appear nonlinearly and the determination of the adaptive law for such parameters is a nontrivial task. In this paper, we propose a new adaptive control method in an effort to tune all the RBF parameters thereby reducing the approximation error and improving control performance. Global boundedness of the overall adaptive system and tracking to within a desired precision are established with the new adaptive controller. Simulations performed on a simple nonlinear system illustrate the approach.

The position/force control of mechanical systems subject to a set of Pfaffian constraints is addressed in this paper. A reduced order dynamical description of such nonholonomic mechanical systems, including the constraints, is developed. Some properties of the dynamic model are then exploited to facilitate the controller design. Based on the theory of guaranteed stability of uncertain systems, a robust control algorithms is derived, guaranteeing the uniform ultimate boundedness of the tracking errors. A detailed numerical example is presented to illustrate the developed method.

In Su and Stepanenko (1995), a hybrid adaptive controller for rigid-link electrically-driven robot manipulators was proposed. Semi-global asymptotic stability of the controller was established in the Lyapunov sense. However, there are two limitations in it. One is that the controller requires the joint velocity measurements, that with the required accuracy can be difficult to realize in practical applications. The other one assumes the boundedness of estimated inertia parameters of the manipulator in order to reduce the computation complexity. In this paper, we propose a modification of the hybrid adaptive controller, which eliminate the above-mentioned limitations. Hence the range of applicability of the method in the above article can be greatly broadened. The capabilities of the proposed control strategies are illustrated through computer simulation.

This paper proposes a technique of iterative dynamic programming to plan minimum energy consumption trajectories for robotic manipulators. The dynamic programming method is modified to perform a series of dynamic programming passes over a small reconfigurable grid covering only a portion of the solution space at any one pass. Although strictly no longer a global optimization process, this iterative approach retains the ability to avoid some poor local minima while avoiding the curse of dimensionality associated with a pure dynamic programming approach. The algorithm has an inherent parallel structure, allowing for reduced computation time on parallel architecture computers. No limiting assumptions are made about the performance index, or function to be optimized. As such, extremely complex functions and constraints are easily handled. Joint actuator and time constraints are considered in this work. The modified dynamic programming approach is verified experimentally by planning and executing a minimum energy consumption path for a Reis V15 industrial manipulator.

This paper addresses the problem of controller design for constrained robots with the consideration of computational efficiency. An adaptive control algorithm, based on the reduced dynamics formulation, is presented for trajectory tracking of an end-effector on a constrained surface with specified constraint forces. It is shown that the control objective can be achieved without exact knowledge of robot dynamics and online calculation of nonlinear dynamic functions. The control algorithm is constructed with at most four control parameters to be adjusted adaptively, and that number is determined independently of the number of degrees of freedom of the robotic manipulators.

In this paper a hybrid adaptive/robust control scheme is proposed for rigid-link electrically-driven robot manipulators in the presence of arbitrary uncertain inertia parameters of the manipulator and the electrical parameters of the actuators. In contrast to the known methods, the presented design requires at most the joint velocity feedback and does not rely on the knowledge of the bounds of complexity functions. Semi-global asymptotic stability of the adaptive/robust controller is established in the Lyapunov sense. Simulation results are included to demonstrate the tracking performance.>

When a common object, attached to multiple robot arms, is cooperatively manipulated to move along a constrained surface, the control task requires the simultaneous control of the motion trajectory of the attached object on the constrained surface; the constrained force due to the contact with the surface; and the internal force exerted by the arms on the object. To accomplish such a control objective, an adaptive sliding mode control algorithm is presented by developing a new concise dynamic model of the system and exploiting its particular properties. Detailed analysis on the tracking properties of the object's position, the constrained force, and the internal force are given. The stability analysis shows that the proposed algorithm can achieve satisfactory tracking performance.>

In this paper the design of adaptive control of rigid-link electrically-driven robot manipulators is addressed in the presence of arbitrary uncertain inertial parameters of the manipulator and the electrical parameters of the actuators. In contrast to the known methods, the presented design requires at most the joint velocity feedback and does not rely on the knowledge of the bounds of complexity functions. Global asymptotic stability of the adaptive controller is established in the Lyapunov sense. Simulation results are included to demonstrate the tracking performance.>

An adaptive tracking control architecture is proposed for a class of continuous-time nonlinear dynamic systems, for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs fuzzy systems, which are expressed as a series expansion of basis functions, to adaptively compensate for the plant nonlinearities. Global asymptotic stability of the algorithm is established in the Lyapunov sense, with tracking errors converging to a neighborhood of zero. Simulation results for an unstable nonlinear plant are included to demonstrate that incorporating the linguistic fuzzy information from human experts results in superior tracking performance.>

Based on a general form for a sliding manifold, two design strategies for adaptive sliding mode control are presented for nonlinear robot manipulator systems. It is shown that, without any prior knowledge of the manipulator parameters under the deterioration of a class of state-dependent input disturbances, the controllers guarantee the occurrence of the sliding mode on the general sliding manifold, which can be a nonlinear or time-varying manifold. In the sliding mode, the desired performance can be obtained by selecting a suitable sliding manifold, which is illustrated, for example, by a nonlinear manifold.