This paper introduces a novel class of length-4N orthonormal scalar wavelets, and presents the theory, implementational issues, and their applications to image compression. We first give the necessary and sufficient conditions for the existence of this class. The parameterized representation of filters with different lengths are then given. Next, we derive new and efficient decomposition and reconstruction algorithms specifically tailored to this class of wavelets. We show that the proposed discrete wavelet transformations are orthogonal and have lower computational complexity than conventional octave-bandwidth transforms using Daubechies' (1989) orthogonal filters of equal length. In addition, we also verify that symmetric boundary extensions can be applied. Finally, our image compression results further confirm that improved performance can be achieved with lower computational cost.

Approximation order, linear phase symmetry, time-frequency localization, regularity, and stopband attenuation are some criteria that are widely used in wavelet filter design. We propose a new criterion called good multifilter properties (GMPs) for the design and construction of multiwavelet filters targeting image compression applications. We first provide the definition of GMPs, followed by a necessary and sufficient condition for an orthonormal multiwavelet system to have a GMP order of at least 1. We then present an algorithm to construct orthogonal multiwavelets possessing GMPs, starting from any length-2N scalar CQPs. Image compression experiments are performed to evaluate the importance of GMPs for image compression, as compared to other common filter design criteria. Our results confirmed that multiwavelets that possess GMPs not only yield superior PSNR performances, but also require much lower computations in their transforms.

A discrete trajectory planner is described which has been shown to be capable of planning optimal trajectories for a six-degree-of-freedom robot with minimum time/energy objective functions and realistic constraints on the joint velocities, joint torques, joint jerks, and hand velocity. It is also flexible enough to handle other objective functions and constraints, provided they can be satisfactorily discretized. An alternative formulation of the discrete trajectory planner is also provided for the efficient generation of optimal trajectories when equal time intervals are required. Once an optimal trajectory is planned offline with the discrete trajectory planner, the open-loop solution can be fed to the online feedback controller for trajectory tracking. Computation time taken by the discrete trajectory planner is acceptable for offline planning purposes. Numerical examples are presented for the Stanford manipulator using all six degrees of freedom.>

A minimum time trajectory planner is proposed for a manipulator arm. A totally discrete approach is adopted, in contrast to other models which use continuous-time but resort to discretization in the computation. The Neuman and Tourassis discrete-dynamic robot model is used to model the robot dynamics. The proposed trajectory planner includes joint-torque constraints to fully utilize the joint actuators. Realistic constraints such as the joint-jerk and joint-velocity constraints are incorporated into the model. The nonlinear optimization problem associated with the planner is partially linearized, which enables the iterative method of approximate programming to be used in solving the problem. Numerical examples for a two-link revolute arm are presented to demonstrate the use of the proposed trajectory planner. It is numerically verified that the convergence of the iterative algorithm is quadratic, and the trajectory planner therefore is computationally efficient. The use of a near-minimum time-cost function is also shown to yield a solution close to that obtained with the true minimum time-cost function.>