Thomas R. Kane

The Use of Kane's Dynamical Equations in Robotics

Extensive experience has shown that the use of general- purpose, multibody-dynamics computer programs for the numerical formulation and solution of equations of motion of robotic devices leads to slow evaluation of actuator forces and torques and slow simulation of robot motions. In this paper, it is shown how improvements in computational efficiency can be effected by using Kanes dynamical equations to formulate explicit equations of motion. To these ends, a detailed analysis of the Stanford Arm is presented in such a way that each step in the analysis serves as an illustrative example for a general method of attack on problems of robot dynamics. Simulation results are reported and are used as a basis for discussing questions of computational efficiency.

HUMAN SELF-ROTATION BY MEANS OF LIMB MOVEMENTS*

Abstract A ‘weightless’ astronaut can alter the orientation of his body in space by moving his limbs in an appropriate manner. The feasibility of employing two particular limb maneuvers, one producing pitch motion, and the other yaw, is established analytically, and quantitative results are presented.

Formulation of dynamical equations of motion

Advances in computer technology have brought into reach the solutions of many dynamics problems previously regarded as excessively complex. However, in order actually to carry out solutions, one must be able to generate computational algorithms in an effective way. In the present paper, this issue is confronted through the discussion of a law of motion that is, in essence, a generalization of Lagrange’s equations. Following the introduction of ‘‘generalized speeds,’’ ‘‘partial angular velocities,’’ and ‘‘partial velocities,’’ the equations of motion are formulated for a simple system in order to illustrate each of these concepts in concrete terms. To provide a basis for comparisons, the equations of motion of the system are then formulated also by employing Lagrange’s equations.

Realistic mathematical modeling of the rattleback

Abstract The rattleback (also called a Celt or wobblestone) is an object which, when placed on a horizontal surface and caused to rotate about a vertical axis, sometimes begins to oscillate, stops turning, and then starts rotating in the direction opposite to that associated with the original motion. Earlier analyses dealing with this phenomenon have been based on a variety of assumptions. In the present work, it is shown by means of numerical solutions of full, non-linear equations of motion that one can construct a realistic mathematical model by assuming rolling without slipping and employing a torque proportional to angular velocity to provide for energy dissipation.

Experimental investigation of an astronaut maneuvering scheme.

Abstract To devise air astronaut maneuvering scheme, one must solve certain problems of dynamics within a framework of restrictions imposed by physiological and psychological limitations of human beings. Experiments involving human test subjects thus play an important role in the design of an astronaut maneuvering system. This paper deals with a series of such experiments, performed to test a maneuvering concept that appears to offer advantages in propellant economy, system weight, reliability, and safety over others proposed heretofore.

AUTOLEV — A New Approach to Multibody Dynamics

AUTOLEV, an interactive symbolic dynamics program based on the method set forth in [1] for formulating equations of motion, differs fundamentally from other multibody dynamics programs in that it gives the user step-by-step control of the equation formulation process. Its unstructured format places virtually no restrictions on the types of dynamical systems that it accommodates, so that one can deal equally easily with one, two, and three dimensional holonomic and nonholonomic systems, closed loops, moving constraints, etc. Moreover, the process of formulating equations of motion is unencumbered by the computer memory limitations and slow run times associated with classical methods of mechanics, and the program thus can be used on a desktop computer.

Locomotion of snakes: a mechanical ‘explanation’

Abstract This paper presents a multibody model of a snake, a model which incorporates a particular assumption about the interaction between the snake and the ground. Solutions of the associated equations of motion produce results consistent with the motion of a real snake, thus lending credibility to the claim that the postulated snake–ground interaction force law has a basis in reality.

DEPLOYMENT AND RETRIEVAL OPTIMIZATION OF A TETHERED SATELLITE SYSTEM

This paper describes the optimization analysis results of deployment and retrieval of a tethered satellite system. The system is composed of two small satellites connected by a long tether. One of the satellites is equipped with a set of thrusters for purposes of control. The optimization analysis is based on the nonlinear equations of motion, and the optimized length law together with the optimized thrust histories are calculated. The optimization is performed with a MATLAB-based multicontroller algorithm. First, the algorithm is used to optimize the phases of deployment and retrieval for a simple model where the tether is represented by a massless rod. Then these results are used as a nominal path for a retrieval involving a more realistic model. When this model is used to simulate retrieval, the system is kept on the nominal path by means of a regulator. The optimization result, compared with results in previous papers, points to improved performance and a significant reduction in fuel consumption.

Estimation and control of tethered satellite systems

This paper describes the analysis of a tethered system during the station-keeping phase. The system is composed of two small satellites connected by a long tether. The satellites are modeled as particles, and the tether is represented by eight rigid, massive rods. The angles between adjacent elements can vary with time. Only measurements at the end bodies are considered, and the angles between the tether segments are estimated by using a reduced-order estimator. The compensator design is based on the linear quadratic regulator algorithm and a steady-state Kalman filter. It is shown that all motion modes are observable with the available measurements and controllable with thrusts on one of the satellites.

Symbolic Generation of Efficient Simulation/Control Routines for Multibody Systems

Techniques for improving the efficiency of simulation subroutines generated with the aid of computer algebra are presented in the form of MACSYMA utility functions.