Rehabilitation Robotics Jumpstation
Thesis - Charles W Wampler
Computer methods in manipulator kinematics, dynamics, and control: a comparative study (1985)
This dissertation seeks to attain the following objectives:
- Develop efficient algorithms for manipulator kinematics and dynamics, including inverse kinematic solutions, actuator torque computation, and equations of motion for simulation. These algorithms form the basic tools for path planning, control, and numerical evaluation of various control schemes.
- Investigate the reduction in computation that can be obtained when the manipulator fits the assumptions of a restricted model incorporating simplifications common to most industrial manipualtors, and estimate the reduction that can be anticipated when the equations are worked out symbolically by doing so for a model of the Stanford Arm.
- Analyze the singularities that can arise in inverse kinematic solutions and develop efficient means of dealing with their presence. This is essential if the solutions are to be used in a real-time control system.
- Present stability proofs for several control schemes, including the conventional joint servo, computed-torque control, resolved-rate control, and resolved-acceleration control. The assumptions and limitations of each analysis are stated, and the effects of kinematical singularities are delineated.
- Compare the expected performance of the conventional joint servo and the computed-torque servo in computer simulations of the Stanford Arm. The analysis includes the nonlinear dynamics and kinematics of the arm, and the computational delay and discrete-time nature of the computed-torque servo.
All dynamical algorithms are based on a modified formulation of Kane's
equations of motion. Accurate operation counts for the algorithms are obtained
directly from computer implementations. A typical result is that for the
computation of actuator torques for a six-degree-of-freedom manipulator, the restricted model
requires 50% fewer multiplications than the general model, and the model of the
Stanford Arm requires 66% fewer multiplications than the general model.
One of the highlights of the thesis is the development of the damped-least
squares approach to handling kinematical singularities, which greatly reduces the joint velocities and accelerations near singularities in exchange for small errors in the path of the manipulator end-effector.