An algorithm is presented for generating near-time-optimal trajectories for an open-kinematic-chain manipulator moving in a cluttered workspace. This is the first algorithm to guarantee bounds on the closeness of an approximation to a time-optimal trajectory. The running time and space required are polynomial in the desired accuracy of the approximation. The user may also specify tolerances by which the trajectories must clear obstacles in the workspace to allow modeling of control errors.>

The authors develop simple, configuration-independent bounds for the Jacobian and the higher order derivatives of the forward kinematic map of a manipulator with revolute and prismatic joints. In doing so they obtain: a simple formula for the higher order derivatives of the forward kinematic map; an easily computable and meaningful metric on the group of rigid-body motions; and useful norms on the joint space of a manipulator. The bounds on the forward kinematic map are practical to implement and have proved to be very useful for trajectory interpolation, space generation, and interpolation of the robot dynamics.>

An algorithm for interpolating workspace trajectories in the joint space of a manipulator having revolute and prismatic joints is described. This algorithm relies on bounds on the derivatives of the kinematic map of such a manipulator derived by the authors (ibid., vol.3, p.1744-9). The algorithm generates interpolates such that user-specified tolerances on position, velocity and acceleration are maintained. This is the first joint space interpolation algorithm to guarantee workspace error bounds on velocity and acceleration. The algorithm includes the prismatic case, which is also novel, and it takes into account factors beyond kinematic errors, making it a practical addition to a robotic manipulator system.>

The authors develop simple configuration-independent bounds on the dynamics of a robot manipulator. In particular, the inertia and gravity tensors and their derivatives of all orders for open-kinematic-chain manipulators. The bounds are useful in dynamics interpolation bounding the Coriolis and centrifugal forces (since these depend on the derivatives of the inertia tensor), suboptimal control, and path planning with dynamical constraints. These bounds can be used for verifying that trajectories satisfy actuator constraints. The bounds on the derivatives of the inertia tensor bound Coriolis and centrifugal forces and determine whether or not they can be ignored along a trajectory. The bounds on the derivatives also permit reliable interpolation of feedforward terms of dynamic compensation in control. In addition, they may also be used to simplify convergence proofs in nonlinear control schemes where detailed estimates of the dynamics are required, and they are useful in a variety of planning and optimization problems to prove the correctness of algorithms.>

A simple and efficient algorithm is developed to generate a 2"-tree (generalized quad-tree) representation of the free configuration space for a manipulator moving in a workspace with obstacles. The algorithm is based on the existence of uniform bounds on the Jacobians relating the differential motions of points on the manipulator to differential joint motions. This representation can be searched to generate a collision-free path and optimized with dynamic constraints to produce an executable trajectory.

An algorithm for interpolating workspace trajectories in the jointspace of a manipulator having revolute joints is described. The algorithm generates an interpolation so that a user-specified tolerance is maintained. In the process of developing this algorithm, it is shown that a particular induced pseudonorm of the Jacobian is bounded by the length of the manipulator and that a similar result holds for all derivatives of the forward kinematic map. The bounds obtained are used in the error analysis of the interpolation algorithm.>

We present a new scheme for the adaptive control of mechanical manipulators along with proof of convergence. This work is an extension of our earlier work [Craig, Hsu and Sastry] [1]. The new scheme does not require the measurement of joint accelerations and needs less computation. We illustrate the theory with some simulations.

A nonlinear phase estimator for a phase-shift keyed (PSK)-modulated carrier has been developed by Viterbi and Viterbi. Their analysis is extended, and an optimal or "matched" nonlinearity is derived for the estimator.