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Paper discusses stability of digital model-reference adaptive control (MRAC) of robotic system or plant that operates at discrete time steps. Command-generator tracker (CGT) concept, originally proposed for continuous-time systems, is applied in discrete-time setting, enabling relaxation of some restrictive assumptions that guarantee stability of system controlled according to resulting algorithm. Likely applications include systems in which sensors and actuators not placed together.

In a space telerobotic service scenario, cooperative motion and force control of multiple robot arms are of fundamental importance. Three paradigms to study this problem are proposed. They are distinguished by the set of variables used for control design. They are joint torques, arm tip force vectors, and an accelerated generalized coordinate set. Control issues related to each case are discussed. The latter two choices require complete model information, which presents practical modeling, computational, and robustness problems. Therefore, focus is on the joint torque control case to develop relatively model independent motion and internal force control laws. The rigid body assumption allows the motion and force control problems to be independently addressed. By using an energy motivated Lyapunov function, a simple proportional derivative plus gravity compensation type of motion control law is always shown to be stabilizing. The asymptotic convergence of the tracing error to zero requires the use of a generalized coordinate with the contact constraints taken into account. If a non-generalized coordinate is used, only convergence to a steady state manifold can be concluded. For the force control, both feedforward and feedback schemes are analyzed. The feedback control, if proper care has been taken, exhibits better robustness and transient performance.

The motion and force control of multiple robot arms manipulating a commonly held object is addressed. A general control paradigm that decouples the motion and force control problems is introduced. For motion control, there are three natural choices: (1) joint torques, (2) arm-tip force vectors, and (3) the acceleration of a generalized coordinate. Choice (1) allows a class of relatively model-independent control laws by exploiting the Hamiltonian structure of the open-loop system; (2) and (3) require the full model information but produce simpler problems. To resolve the nonuniqueness of the joint torques, two methods are introduced. If the arm and object models are available, the allocation of the desired end-effector control force to the joint actuators can be optimized; otherwise the internal force can be controlled about some set point. It is shown that effective force regulation can be achieved even if little model information is available.

A new class of exponentially stabilizing control laws for joint level control of robot arms is discussed. Closed-loop exponential stability has been demonstrated for both the set point and tracking control problems by a slight modification of the energy Lyapunov function and the use of a lemma which handles third-order terms in the Lyapunov function derivatives. In the second part, these control laws are adapted in a simple fashion to achieve asymptotically stable adaptive control. The analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and uses a parameterization based on physical (time-invariant) quantities.

Multiple robot arms moving a commonly held object can be viewed as complex actuators whose purpose is to provide net forces and moments to the object. These forces and moments can be used to control the orientation, or attitude, of the object via the Euler equation describing attitude evolution in response to applied moments at the mass center. In contrast to the common approach that feedback-linearizes the attitude dynamics to a double integrator form with respect to some three-parameter local representation of orientation, the authors control the object using a globally nonsingular representation. Using an energy-motivated Liapunov function, globally stable control of attitude is shown.

An approach using a globally nonsingular representation is proposed for the attitude control problem of a rigid body. The attitude dynamics are described by the nonlinear Euler equation together with the nonlinear kinematic equations which relate a representation of attitude to the angular velocity of the body. When this approach is combined with an energy-motivated Lyapunov function, a large class of globally stable attitude control laws can be derived. This class includes model-independent tracking control, model-dependent tracking control, and adaptive control, allowing tradeoffs between controller complexity, attainable performance, and available model information.

The author discusses a generalization of hyperstability to systems in Hilbert space and its application to finite-dimensional stabilizing compensator design. The basic idea is to characterize tolerable perturbations in terms of the passivity of the nominal closed-loop system. Controllers achieving the required closed-loop passivity property can then be designed using H(infinity)-optimization. In particular, the author presents a design procedure for a stabilizing a finite-dimensional compensator for a given infinite-dimensional system.

The authors consider several possible control structures for multiple-arm systems by regarding either joint torques, tip force, or a generalized acceleration of the control input. They emphasize the first case, since a class of relatively model-independent control laws can be generated for both motion and internal force control. The recently developed move/squeeze orthogonal subspace decomposition coupled with the energy Lyapunov function formulation provides a basic analytical framework within which motion and force control are considered as independent problems. Simulation results of two three-link planar arms are included to demonstrate good transient performance for both motion and force that can be attained with the full dynamics control paradigm.

Existence theorem proved for nonlinear systems. Report discusses mathematical requirements for existence of solution to minimum-time control problem for robotic manipulator that obeys nonlinear equations of motion.

A class of joint-level control laws for all-revolute robot arms is introduced. The analysis is similar to the recently proposed energy Liapunov function approach except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. By using energy Liapunov functions with the modified potential energy, a much simpler analysis can be used to show closed-loop global asymptotic stability and local exponential stability. When Coulomb and viscous friction and model parameter errors are present, a sliding-mode-like modification of the control law is proposed to add a robustness-enhancing outer loop. Adaptive control is also addressed within the same framework. A linear-in-the-parameters formulation is adopted, and globally asymptotically stable adaptive control laws are derived by replacing the model parameters in the nonadaptive control laws by their estimates.

A technique of robust stability analysis for multivariable control systems is introduced. Existing tools in the literature are mostly based on small gain type of conditions such as the H(infinity)-norm or mu measure. In contrast, the approach presented is motivated by passivity theory. The natural energy Lyapunov function associated with a passive system allows robustness to be analyzed with Lyapunov stability theory. Consequently, nonlinear and time-varying perturbations can be considered within the same framework. For unstructured uncertainties, the robustness margin is characterized in terms of an index related to the Hermitian part of a transfer function. If the uncertainties contain additional diagonal structure, stability margins are obtained for variations of each uncertain block in both positive and negative directions. Applications of this robustness analysis technique are illustrated.