Hwee Huat Tan

Minimum time trajectory planner for the discrete dynamic robot model with dynamic constraints

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. >

A discrete trajectory planner for robotic arms with six degrees of freedom

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. >

On a family of orthonormal scalar wavelets and related balanced multiwavelets

For a family of length-4N orthonormal scalar wavelet filters that has been shown to be closely related to symmetric/antisymmetric orthonormal multifilters (SAOMFs), a sufficient and necessary condition is given for their construction. A near-linear criterion is then provided for constructing balanced multiwavelet filters related to these scalar filters. Numerical results are presented to demonstrate the potential usefulness of this criterion.

Some properties of symmetric-antisymmetric orthonormal multiwavelets

We analyze the discrete multiwavelet transform using symmetric-antisymmetric orthonormal multifilters (SAOMFs) and prove that for any even-length SAOMF, we can always find an odd-length SAOMF such that the implementation of discrete multiwavelet transform using either the even-length or the odd-length SAOMF produces identical output for a given input signal if the sum/difference prefilter is chosen.

A State-Space Partitioning Method for Pricing High-Dimensional American-Style Options

The pricing of American-style options by simulation-based methods is an important but difficult task primarily due to the feature of early exercise, particularly for high-dimensional derivatives. In this paper, a bundling method based on quasi-Monte Carlo sequences is proposed to price high-dimensional American-style options. The proposed method substantially extends Tilleys bundling algorithm to higher-dimensional situations. By using low-discrepancy points, this approach partitions the state space and forms bundles. A dynamic programming algorithm is then applied to the bundles to estimate the continuation value of an American-style option. A convergence proof of the algorithm is provided. A variety of examples with up to 15 dimensions are investigated numerically and the algorithm is able to produce computationally efficient results with good accuracy.

A computationally efficient state-space partitioning approach to pricing high-dimensional American options via dimension reduction

This paper studies the problem of pricing high-dimensional American options. We propose a method based on the state-space partitioning algorithm developed by Jin et al. (2007) and a dimension-reduction approach introduced by Li and Wu (2006). By applying the approach in the present paper, the computational efficiency of pricing high-dimensional American options is significantly improved, compared to the extant approaches in the literature, without sacrificing the estimation precision. Various numerical examples are provided to illustrate the accuracy and efficiency of the proposed method. Pseudcode for an implementation of the proposed approach is also included.

A new multifilter design property for multiwavelet image compression

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 path/trajectory planner for robotic arms

An interesting and challenging problem in robotics is the off-line determination of the minimum cost path along which an end effector should move from a given initial to a given final state. This paper presents a discrete minimum cost path/trajectory planner which provides a general solution and allows for a range of constraints such as bounds on joint coordinates, joint velocities, joint torques and joint jerks. To demonstrate the practicability and feasibility of the planner, simulation results are presented for the Stanford manipulator using three and then the full six of its degrees of freedom. Simulation runs with two-link planar arms are also presented to enable a comparison with previously published results.

Smooth piecewise biquartic surfaces from quadrilateral control polyhedra with isolated n-sided faces

Abstract The modelling of surfaces by piecewise bipolynomial patches has important applications in computer-aided design and computer graphics. However, existing methods do not always work for control polyhedra with arbitrary topology. A method is proposed that uses only piecewise biquartics which will work for control polyhedra with mostly quadrilateral faces and isolated n -sided faces ( n ≠ 4). The surfaces are modelled by converting the control points to Bezier points for each patch using a blending matrix. The blending matrices are constructed from generalized biquartic B-spline blending functions. The domain of definition of these is a nonplanar rectangular surface mesh in 3D Euclidean space. The rectangular mesh consists of rectangular faces whose vertices can have an arbitrary number of edges. The construction of the generalized biquartic B-spline blending functions is described. The resulting surface is geometrically smooth around the extraordinary vertices and parametrically smooth otherwise. Furthermore, free parameters are available for manipulating the shape of the surface locally around the extraordinary points.

When should venture capitalists exit their investee companies

Purpose - – Exit strategies are critical for external private equity holders, such as venture capitalists and business angels, to receive investment returns successfully. The paper models the exit decision as a fixed date with the option to exit early, and develop an approach to help private equity holders determine an optimal early exit region based on a target equity value and the time remaining. Design/methodology/approach - – The paper sets up a continuous time model to derive analytical solutions and apply simulations to numerical examples in this study. Findings - – By numerically analyzing the nature of the solution the paper illustrates that a higher return drift of the investee company, a lower return volatility of the investee company, and a higher target return of the private equity holder results a smaller early exit region. Originality/value - – This study helps determine the optimal time of stopping investments, and provides venture capitalists with a usable way to make exit decisions.