Robot control using adaptive transformations

Lobbezoo, Andrew; Bruijn, P.M.; Davies, M. S.; Dunford, W.G.; Lawrence, P.D.; Lemke, H.R. van Nauta

doi:10.1109/56.781

Cited by 6 publications

References 6 publications

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A discrete‐time optimal adaptive control law for a robot arm

Marchand¹,

Lawrence²,

Cherchas³

1989

Optim Control Appl Methods

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The equations of motion describing a robot's dynamics are coupled and non-linear, making the design of an optimum controller difficult using classical techniques. In this work a n explicit adaptive control law is proposed based on a discrete linear model for each link and on the minimization of a quadratic performance criterion for position error and total control effort. The system parameters are recursively estimated at each control step by use of least squares, with a typical sample time of 0.02 s. A computer simulation of the resulting scheme is performed to evaluate the controller. The simulation model, based on the first three links of an existing robot, includes detailed motor dynamics and treats the wrist assembly as a load mass. Simulated test paths requiring movement of the outer two links indicate that the controller adapts and that its behaviour is stable and convergent.

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A discrete‐time optimal adaptive control law for a robot arm

Marchand¹,

Lawrence²,

Cherchas³

1989

Optim Control Appl Methods

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An adaptive scheme for robot joint trajectory generation

Hsia

Guo

1990

J. Robotic Syst.

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It has been shown recently that robot inverse kinematic transformation can be easily carried out by using a nonlinear dynamic system called “joint space command generator.” In this paper, an adaptive version of the command generator is proposed. The main feature of this command generator is that the inverse Jacobian is estimated on‐line (using least‐squares algorithms), thus the explicit form of the inverse Jacobian is not required. Since the Jacobian is dependent on the end‐effector orientation representation, the adaptive command generator is then inherently flexible in accommodating any choice of orientation representation during Cartesian trajectory planning. The only knowledge required is the forward kinematics of the robot. Thus inverse kinematic transformation of robot trajectories can be carried out with a minimum amount of kinematic information. Extensive simulation studies of the proposed scheme have been carried out which showed that the adaptive command generator is computationally feasible and highly accurate. Different orientation representations have been tested with equal success. Some typical simulation results are presented to illustrate the performance of the adaptive command generator.

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Computer generation of symbolic kinematics for robot manipulators

Cain

Herrera-Bendezu

1992

J. Robotic Syst.

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Computer generation of symbolic solutions for the direct and inverse robot kinematics is a desired capability not previously available to robotics engineers. In this article, we present a methodology for the design of a software system capable of solving the direct and inverse kinematics for n degree of freedom (do0 manipulators in symbolic form. The inputs to the system are the Denavit-Hartenberg parameters of the manipulator. The outputs of the system are the direct and inverse kinematics solutions in symbolic form. The system consists of a symbolic processor to perform matrix and algebraic manipulations and an expert system to solve the class of nonlinear equations involved in the solution of the inverse kinematics problem. The system can be used to study robot kinematics configurations whose inverse kinematics solutions are not known to exist a priori. Two examples are included to illustrate its capabilities. The first example provides explicit analytical solutions, previously believed nonexistent, for a 3 dof manipulator. A second example is included for a robot whose inverse kinematics solution requires intensive algebraic manipulations.

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Robot control using adaptive transformations

Cited by 6 publications

References 6 publications

A discrete‐time optimal adaptive control law for a robot arm

A discrete‐time optimal adaptive control law for a robot arm

An adaptive scheme for robot joint trajectory generation

Computer generation of symbolic kinematics for robot manipulators

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