Jean-Jacques E. Slotine

On the adaptive control of robot manipulators

A new adaptive robot control algorithm is derived, which consists of a PD feedback part and a full dynamics feedfor ward compensation part, with the unknown manipulator and payload parameters being estimated online. The algorithm is computationally simple, because of an effective exploitation of the structure of manipulator dynamics. In particular, it requires neither feedback of joint accelerations nor inversion of the estimated inertia matrix. The algorithm can also be applied directly in Cartesian space.

Gaussian networks for direct adaptive control

A direct adaptive tracking control architecture is proposed and evaluated 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 a network of gausian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness exhibited by the nonlinear functions, the algorithm is proven to be stable, with tracking errors converging to a neighborhood of zero. A constructive procedure is detailed, which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy. A stable weight adjustment mechanism is then determined using Lyapunov theory. The network construction and performance of the resulting controller are illustrated through simulations with an example system.

Controllability of complex networks

The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system’s entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network’s degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes.

Stable adaptive teleoperation

A study is made of how the existence of transmission time delays affects the application of advanced robot control schemes to effective force-reflecting telerobotic systems. This application best exploits the presence of the human operator while making full use of available robot control technology and computing power. A physically motivated, passivity-based formalism is used to provide energy conservation and stability guarantees in the presence of transmission delays. The notion of wave variable is utilized to characterize time-delay systems and leads to a configuration for force-reflecting teleoperation. The effectiveness of the approach is demonstrated experimentally. Within the same framework, an adaptive tracking controller is incorporated for the control of the remote robotic system and can be used to simplify, transform, or enhance the remote dynamics perceived by the operator. >

Sliding controller design for non-linear systems

Abstract New results are presented on the sliding control methodology introduced by Slotine and Sastry (1983) to achieve accurate tracking for a class of non-linear time-varying multivariate systems in the presence of disturbances and parameter variations. An explicit trade-off is obtained between tracking precision and robustness to modelling uncertainty : tracking accuracy is sot according to the extent, of parametric uncertainty and the frequency range of unmodelled dynamics. The trade-off is further refined to account for time-dependence of model uncertainty.

Adaptive manipulator control: A case study

The authors previous work (1986, 1987) utilized the particular structure of manipulator dynamics to develop a simple, globally convergent adaptive controller for manipulator trajectory control problems. After summarizing the basic algorithm, they demonstrate the approach on a high-speed two-degree-of-freedom semi-direct-drive robot. They show that the dynamic parameters of the manipulator, assumed to be initially unknown, can be estimated within the first half second of a typical run, and that accordingly, the manipulator trajectory can be precisely controlled. These experimental results demonstrate that the adaptive controller enjoys essentially the same level of robustness to unmodeled dynamics as a PD (proportional and differential) controller, yet achieves much better tracking accuracy than either PD or computed-torque schemes. Its superior performance for high-speed operations, in the presence of parametric and nonparametric uncertainties, and its relative computational simplicity, make it an attractive option both for addressing complex industrial tasks, and for simplifying high-level programming of more standard operations. >

On contraction analysis for non-linear systems

This paper derives new results in non-linear system analysis using methods inspired from fluid mechanics and differential geometry. Based on a differential analysis of convergence, these results may be viewed as generalizing the classical Krasovskii theorem, and, more loosely, linear eigenvalue analysis. A central feature is that convergence and limit behavior are in a sense treated separately, leading to significant conceptual simplifications. The approach is illustrated by controller and observer designs for simple physical examples.

The robust control of robot manipulators

A new scheme is presented for the accurate tracking control of robot manipulators. Based on the more general suction control methodology, the scheme addresses the following problem: Given the extent of parametric uncertainty (such as imprecisions or inertias, geometry, loads) and the frequency range of unmodeled dynamics (such as unmodeled structural modes, neglected time delays), design a nonlinear feedback controller to achieve optimal tracking performance, in a suitable sense. The methodology is compared with standard algorithms such as the computed torque method and is shown to combine in practice improved performance with simpler and more tractable controller designs.

Adaptive sliding controller synthesis for non-linear systems

Classical ‘sliding mode control’, as investigated mostly in Soviet literature, features excellent robustness properties in relation to parametric uncertainty, but presents several important drawbacks that severely limit its practical applicability. These drawbacks, including large control authority and control chattering, were remedied by Slotine and Sastry (1983) and Slotine (1984) by replacing control switching at a fixed sliding surface by a smooth control interpolation in a boundary layer neighbouring a time-varying sliding surface. This avoids the excitation of high-frequency unmodelled dynamics, and leads to an explicit trade-off between model uncertainty and controller tracking performance. The present paper examines how to further improve performance by effectively coupling on-line parameter estimation to sliding controller design. The boundary layer concept leads to a compact measure of the quality of parameter estimation, and provides a consistent rule on when to stop adaptation. The approach is...

Telemanipulation with Time Delays

In this paper we survey the development of the wave variable concept and examine wave-based teleoperation. We study the behavior of force reflecting systems under unknown but constant transmission delays, ranging from periods less than the human reaction time to several seconds. Passive transmission procedures guarantee system stability, but wave reflections and spurious dynamics may interfere with normal operation. Using wave variables for the analysis and implementation, and making appropriate design choices, a system with consistent and predictable behavior is constructed. This design methodology aims to create a virtual tool which accounts for the implicit limitations imposed by the delay. These developments also form the basis for extensions to wave-based prediction and application to variable delays, such as those inherent to Internet-based telemanipulation.