Mark W. Spong

Bilateral control of teleoperators with time delay

A control law for teleoperators is presented which overcomes the instability caused by time delay. By using passivity and scattering theory, a criterion is developed which shows why existing bilateral control systems are unstable for certain environments, and why the proposed bilateral control law is stable for any environment and any time delay. The control law has been implemented on a single-axis force-reflecting hand controller, and preliminary results are shown. To keep the presentation clear, a single-degree-of-freedom (DOF) linear time-invariant (LTI) teleoperator system is discussed. Nevertheless, results can be extended, without loss of generality, to an n-DOF nonlinear teleoperation system. >

Robot Modeling and Control

Preface. 1. Introduction. 2. Rigid Motions and Homogeneous Transformations. 3. Forward and Inverse Kinematics. 4. Velocity Kinematics-The Jacobian. 5. Path and Trajectory Planning. 6. Independent Joint Control. 7. Dynamics. 8. Multivariable Control. 9. Force Control. 10. Geometric Nonlinear Control. 11. Computer Vision. 12. Vision-Based Control. Appendix A: Trigonometry. Appendix B: Linear Algebra. Appendix C: Dynamical Systems. Appendix D: Lyapunov Stability. Index.

Bilateral teleoperation: An historical survey

This survey addresses the subject of bilateral teleoperation, a research stream with more than 50 years of history and one that continues to be a fertile ground for theoretical exploration and many applications. We focus on the control theoretic approaches that have been developed to address inherent control problems such as delays and information loss. Exposure to several concurrent applications is provided, and possible future trends are outlined.

The swing up control problem for the Acrobot

Underactuated mechanical systems are those possessing fewer actuators than degrees of freedom. Examples of such systems abound, including flexible joint and flexible link robots, space robots, mobile robots, and robot models that include actuator dynamics and rigid body dynamics together. Complex internal dynamics, nonholonomic behavior, and lack of feedback linearizability are often exhibited by such systems, making the class a rich one from a control standpoint. In this article the author studies a particular underactuated system known as the Acrobot: a two-degree-of-freedom planar robot with a single actuator. The author considers the so-called swing up control problem using the method of partial feedback linearization. The author gives conditions under which the response of either degree of freedom may be globally decoupled from the response of the other and linearized. This result can be used as a starting point to design swing up control algorithms. Analysis of the resulting zero dynamics as well as analysis of the energy of the system provides an understanding of the swing up algorithms. Simulation results are presented showing the swing up motion resulting from partial feedback linearization designs. >

Passive Bilateral Teleoperation With Constant Time Delay

We propose a novel control framework for bilateral teleoperation of a pair of multi-degree-of-freedom nonlinear robotic systems under constant communication delays. The proposed framework uses the simple proportional-derivative control, i.e., the master and slave robots are directly connected via spring and damper over the delayed communication channels. Using the controller passivity concept, the Lyapunov-Krasovskii technique, and Parsevals identity, we can passify the combination of the delayed communication and control blocks altogether robustly, as long as the delays are finite constants and an upper bound for the round-trip delay is known. Having explicit position feedback through the delayed P-action, the proposed framework enforces master-slave position coordination, which is often compromised in the conventional scattering-based teleoperation. The proposed control framework provides humans with extended physiological proprioception, so that s/he can affect and sense the remote slave environments mainly relying on her/his musculoskeletal systems. Simulation and experiments are performed to validate and highlight properties of the proposed control framework

An integral manifold approach to the feedback control of flexible joint robots

The control problem for robot manipulators with flexible joints is considered. The results are based on a recently developed singular perturbation formulation of the manipulator equations of motion where the singular perturbation parameter µ is the inverse of the joint stiffness. For this class of systems it is known that the reduced-order model corresponding to the mechanical system under the assumption of perfect rigidity is globally linearizable via nonlinear static-state feedback, but that the full-order flexible system is not, in general, linearizable in this manner. The concept of integral manifold is utilized to represent the dynamics of the slow subsystem. The slow subsystem reduces to the rigid model as the perturbation parameter µ tends to zero. It is shown that linearizability of the rigid model implies linearizability of the flexible system restricted to the integral manifold. Based on a power series expansion of the integral manifold around µ = 0, it is shown how to approximate the feedback linearizing control to any order in µ. The result is then an approximate feedback linearization which, assuming stability of the fast variables, linearizes the system for all practical purposes.

Energy based control of the Pendubot

This paper presents the control of an underactuated two-link robot called the Pendubot. We propose a controller for swinging the linkage and raise it to its uppermost unstable equilibrium position. The balancing control is based on an energy approach and the passivity properties of the system.

Adaptive motion control of rigid robots: a tutorial

An account is given of several adaptive control results for rigid robot manipulators. The intention is to lend some perspective to the growing list of adaptive control results for manipulators by providing a unified framework for comparison of those adaptive control algorithms which have been shown to be globally convergent. In most cases the authors are able to simplify the derivations and proofs of these results as well.<<ETX>>

On the robust control of robot manipulators

A simple robust nonlinear control law for n-link robot manipulators is derived using the Lyapunov-based theory of guaranteed stability of uncertain systems. The novelty of this result lies in the fact that the uncertainty bounds needed to derive the control law and to prove uniform ultimate boundedness of the tracking error depend only on the inertial parameters of the robot. In previous results of this type, the uncertainty bounds have depended not only on the inertia parameters but also on the reference trajectory and on the manipulator state vector. The presented result also removes previous assumptions regarding closeness in norm of the computed inertia matrix to the actual inertial matrix. The design used thus provides the simplest such robust design available to date. >

Hybrid impedance control of robotic manipulators

The inclusion of force information in the control of robots increases their adaptability to uncertain environments, such as are found in deburring, grinding, and assembly tasks. The authors present a foundation for force control strategies, in view of the fact that the type of control strategy that is employed depends fundamentally on the characteristics of the environment. A general control approach is introduced, called hybrid impedance control which in its simplest forms reduces the operational space control of O. Khatib and J. Burdick (1986), or to N. Hogans (1985) impedance control. The control law is formulated in a general enough fashion, however, to allow for higher order controllers. >