Performance models for robot manipulators.

In this thesis, the concept of performance models for manipulators is introduced and defined. Performance models are used to reduce the computational burden associated with the motion planning of manipulators where manipulator dynamics and actuator constraints have to be taken into account. A performance model for a robot manipulator is a mathematical representation of a subset of the feasible motions of the manipulator, i.e., all those motions which satisfy the manipulator dynamics and meet the actuator constraints. A performance model is conservative if it concludes only a small subset of the feasible motions. There are many performance models that can be constructed, each with varying degrees of conservativeness and computational complexity. Generally, these two qualities are contradictory. The performance model considered in the thesis consists of a pair of sets $\{$B,A(q, v)$\}$. The feasibility of a motion specified by the joint-positions, joint-velocities and the joint accelerations of the manipulator at time t, (q(t), v(t), a(t)), is implied by the inclusions (q(t), v(t)) $\in$ B and a(t) $\in$ A(q(t), v(t)). The standard industrial model of specifying the limits on the magnitudes of the components of q(t), v(t) and a(t) is an extremely conservative but simple performance model. On other hand, by using the closed form inverse dynamics of the manipulator, it is also possible to express the full range of feasible motions by a pair $\{$B,A(q, v)$\}$. The choices proposed for $\{$B,A(q, v)$\}$ achieve a good trade-off between these extremes of conservativeness and computational complexity. In $\{$B,A(q, v)$\}$, the Coriolis/centrifugal terms in the equations of motion are replaced by bounds which depend on $\Vert$v$\Vert\sp2$ only, where $\Vert\cdot\Vert$ is a scaled infinity norm. The effect of the inertial terms is characterized by A(q, v) in the form of a polyhedron. The theoretical basis and computational procedures for determining $\{$B,A(q, v)$\}$ are described in detail. Two extremely different manipulators: the PUMA 560 (3-D Model) and the MIT Direct Drive Arm are used as examples.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105183/1/9116180.pdfDescription of 9116180.pdf : Restricted to UM users only