Kenneth Kreutz

On manipulator control by exact linearization

Comments on the application to rigid link manipulators of geometric control theory, resolved acceleration control, operational space control, and nonlinear decoupling theory are given, and the essential unity of these techniques for externally linearizing and decoupling end effector dynamics is discussed. Exploiting the fact that the mass matrix of a rigid link manipulator is positive definite, and the fact that there is an independent input for each degree of freedom, it is shown that a necessary and sufficient condition for a locally externally linearizing and output decoupling feedback law to exist is that the end effector Jacobian matrix be nonsingular. >

Motion and force control for multiple cooperative manipulators

The authors address the problem of motion and force control of multiple robot arms manipulating an object. A general control paradigm that decouples the motion and force control problems is introduced. For motion control, different control strategies are constructed on the basis of control input variables. There are three natural choices: joint torques, arm tip force vectors, and the acceleration of a generalized coordinate. The first choice allows relatively model-independent control by exploiting the Hamiltonian structure of the open-loop system. The latter two require the full model information but produce simpler control design problems. The motion control determines the joint torque only to within a manifold, owing to the multiple-arm kinematic constraint. 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. The other possibility is to control the internal force about some set point. Effective force regulation can be achieved with little model information.<<ETX>>

High level language-based robotic control system

This invention is a robot control system based on a high level language implementing a spatial operator algebra. There are two high level languages included within the system. At the highest level, applications programs can be written in a robot-oriented applications language including broad operators such as MOVE and GRASP. The robot-oriented applications language statements are translated into statements in the spatial operator algebra language. Programming can also take place using the spatial operator algebra language. The statements in the spatial operator algebra language from either source are then translated into machine language statements for execution by a digital control computer. The system also includes the capability of executing the control code sequences in a simulation mode before actual execution to assure proper action at execution time. The robots environment is checked as part of the process and dynamic reconfiguration is also possible. The languages and system allow the programming and control of multiple arms and the use of inward/outward spatial recursions in which every computational step can be related to a transformation from one point in the mechanical robot to another point to name two major advantages.

Load Balancing and Closed Chain Multiple Arm Control

We give the general dynamical equations for several rigid link manipulators rigidly grasping a commonly held rigid object. It is shown that the number of lost arm configuration degrees of freedom due to imposing the closed loop kinematic constraints is the same as the number of degrees of freedom gained for controlling the internal forces of the closed chain system. This number is equal to the dimension of the kernel of the Jacobian operator which transforms contact forces to the net forces acting on the held object, and it is shown that this kernel can be identified with the subspace of controllable internal forces of the closed chain system. Control of these forces allows one to regulate the grasping forces imparted to the held object or to control the load taken by each arm. It is shown that the internal forces can be influenced without affecting the control of the configuration degrees of freedom, and that this fact is independent of control law choice and involves only kinematical information about each arm. Control laws of feedback linearization type are shown to be useful for controlling the location and attitude of a frame fixed with respect to the held object, while simultaneously controlling the internal forces of the closed chain system. Since the kernel describing the internal forces subspace depends only on the relative location of arm tip contact points, force feedback can be used to feedback linearize and control the system even when the held object has unknown mass properties.

A spatial operator algebra for manipulator modeling and control

The spatial operator algebra developed by the authors for modeling control and trajectory design of manipulation is discussed, with emphasis on the analytical formulation of the operator algebra and its simple implementation in the Ada programming language. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of the manipulator. Inversion of operators can be efficiently obtained using techniques of recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus, the transition from an abstract problem formulation and solution to the detailed mechanization of specific algorithm is greatly simplified.<<ETX>>

Stability analysis of multiple rigid robot manipulators holding a common rigid object

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.<<ETX>>

Attitude Control of an Object Commonly Held by Multiple Robot Arms: A Lyapunov Approach

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 3-parameter local representation of orientation, we control the object using a globally nonsingular representation. Using an energy motivated Lyapunov function, globally stable control of attitude can be shown.

Globally stable control laws for the attitude maneuver problem: tracking control and adaptive control

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.<<ETX>>

A New Class of Energy Based Control Laws for Revolute Robot Arms: Tracking Control, Robustness Enhancement and Adaptive Control

A new class of joint level control laws for all-revolute robot arms is introduced in this paper. The analysis is similar to the recently proposed energy Lyapunov function approach [1, 2], except that the closed loop potential function is shaped in accordance with the underlying joint space topology. By using energy Lyapunov functions with the modified potential energy, a much simpler analysis can be employed 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 non-adaptive control laws by their estimates.

Dynamics and Coordination of Multiple Robot Arms Moving a Common Task Object

This paper presents one phase of some of our recent work in the area of cooperative dual arm control. The focus is on the fundamental properties of closed chain systems that represent multiple robot arms manipulating a commonly held task object, together with some of the control and dynamics issues that arise as a consequence of these properties.