Michael W. Walker

Estimating 3-D location parameters using dual number quaternions

This paper describes a new algorithm for estimating the position and orientation of objects. The problem is formulated as an optimization problem using dual number quaternious. The advantage of using this representation is that the method solves for the location estimate by minimizing a single cost function associated with the sum of the orientation and position errors and thus is expected to have a better performance on the estimation, both in accuracy and in speed. Several forms of sensory information can be used by the algorithm. That is, the measured data can be a combination of measured points on an object’s surfaces and measured unit direction vectors located on the object. Simulations have been carried out on a Compaq 386/20 computer and the SiIIIUkItiOU reSUltS are analyzed. 0 1991 Academic press, inc.

On the dynamics of contact between space robots and configuration control for impact minimization

Contact between free-flying space robots, and the minimization of the impulse at contact are studied. A general approach for modeling systems with a moving base is presented. In particular, the formulation of the dynamical equations of motion for a space-based manipulator system with external applied forces are considered. The new equation of motion is then used to derive a dynamical contact model. Unlike previous approaches, the analysis takes into account both relative translational and rotational motions between contacting bodies. An analysis of the dynamical contact model reveals that the impulse at contact could be minimized by the optimization of a scalar cost function. Two approaches to the Cartesian space planning problem for space-based systems are discussed. A joint space planning strategy that achieves both trajectory tracking and impact minimization is proposed. Simulation results for a fifteen-degree-of-freedom (DOF) space robot are presented. >

Adaptive coordinated motion control of two manipulator arms

An adaptive controller is presented for the coordinated motion control of two manipulators handling an object of unknown mass. Global convergence in tracking of both position and internal force trajectories of the object is proved, assuming perfect models for both manipulators. The computational algorithm is similar to the Newton-Euler inverse dynamics algorithm with complexity linear in the number of links in the manipulators. A significant feature of the control method is that both manipulators use the identical computational algorithm. Thus, the concept of master/slave relationship between the two manipulators is avoided. Two simulations are presented. The first assumes an ideal model for each manipulator. As expected, the controller is stable and provides excellent tracking ability of the manipulator. The second simulation investigates the effects of modeling errors in the mass properties of each arm. The position trajectories track very close to their desired values; however, they never completely converge.<<ETX>>

Adaptive control of space-based robot manipulators

A control method is presented that achieves globally stable trajectory tracking in the presence of uncertainties in the inertial parameters of the system. The 15-degree-of-freedom (DOF) system dynamics are divided into two components: a 9-DOF invertible portion and 6-DOF noninvertible portion. A controller is then designed to achieve trajectory tracking of the invertible portion of the system, which consists of the manipulator joint positions and the orientation of the base. The motion of the noninvertible portion is bounded but otherwise unspecified. This portion of the system consists of the position of the robots base and the position of the reaction wheels. A simulation is presented to demonstrate the effectiveness of the controller. A quadratic polynomial is used to generate the desired trajectory to illustrate the trajectory tracking capability of the controller. >

Basis sets for manipulator inertial parameters

An approach to the problem of finding the minimum number of inertial parameters of the robot manipulator dynamic equations of motion is presented. Based on the energy difference equation, it is equally applicable to serial-link graph-structured manipulators. The authors prove that the minimum number of parameters can be obtained directly from an energy difference equation rather than the dynamic equations of motion. They present a method for the identification of the minimum number of basis vectors which span the vector space containing the components of inertial parameters present in the equations of motion. Simulations are presented and the method is evaluated. The method is conceptually simple, computationally efficient and easy to implement. In particular, the manipulator kinematics and the joint positions and velocities are the only inputs to the algorithm.<<ETX>>

Identifying the independent inertial parameter space of robot manipulators

This paper presents a new approach to the problem of finding the minimum number of inertial parameters of robot manipulator dynamic equations of motion. Based upon the energy difference equation, it is equally applica ble to serial link manipulators as well as graph structured manipulators. The method is conceptually simple, compu tationally efficient, and easy to implement. In particular, the manipulator kinematics and the joint positions and velocities are the only inputs to the algorithm. Applica tions to a serial link and a graph structured manipulator are illustrated.

An efficient algorithm for the adaptive control of a manipulator

A novel algorithm is described for the adaptive control of a robot manipulator which may contain closed kinematic loops. The algorithm identifies the mass properties of each link and the viscous friction coefficients for each joint of the manipulator. It is similar to the Newton-Euler inverse dynamics algorithm and hence obtains its computational efficiency through the recursive nature of the algorithm.<<ETX>>

Manipulator kinematics and the epsilon algebra

A new algebra is defined for use in problems of manipulator kinematics. With this algebra the solution to the inverse kinematics problem can be solved for any time derivative of the joint position using the same program by simply changing the order of the algebra. An example Ada program is used for illustration.

Satellite Stabilization using Space Leeches

This paper presents the control algorithm for a satellite stabilization using a space leech. The space leech is assumed to have n reaction wheels with known moments of inertia about their axis of rotation. All mass properties of the satellite are assumed unknown The proposed control algorithm brings the satellite to a specified attitude trajectory.

An articulated-body model for a free-flying robot and its use for adaptive motion control

We synthesize an adaptive motion control law for a free-flying robot with no external forces or moments. The basic idea is to make use of the articulated part of the space robot to control the position and orientation of the end-effector in an inertial frame. The inertia parameters for the robot end-effector and load are assumed to be a priori unknown. The articulated-body model is linear in the unknown parameters, so that an adaptive control law is developed. A novel feature of our approach is that the parameter estimates are obtained using momentum integrals only. In addition, we use unit quaternions to represent orientation errors. The stability properties of the adaptive control law is shown using Lyapunov stability theory. Computer simulations of an example 12 degrees of freedom space robot system are presented.