This paper proposes a novel control scheme called the ZMM control for generating any desired motion for a family of under-actuated robots with instability such as gymnastics robots and robotic puppets having a single leg pivoted at the floor. This pivotal ankle joint can not be actuator-driven but is passive with a rotary damper. Therefore these robots are intrinsically unstable under the effect of gravity and considered to be under-actuated and nonholonomically constrained. This paper first introduces an (n $1)-dimensional configuration manifold for such robots with n joints, which is called the ZMM (zero moment manifold) and defined as a set of joint angle vectors that satisfy zero of the rotational moment around the first ankle joint. It is shown theoretically that any motion starting from any given posture on a subset of the ZMM and targeting to a desired form of motion can be stabilized by using a coordinated control composed of gravity compensation for other joints except the ankle and PD feedback despite of the existence of a nonholonomic constraint. The effectiveness of the proposed control scheme is verified by numerical simulation and experimental results using a gymnastics robot with four joints.

This paper discusses the perfect reconstruction (PR) condition of a maximally decimated block filter bank, which uses cyclic convolutions instead of linear convolutions used in the usual filter banks. This type of filter bank is particularly useful for subband coding for image data. It is observed that the PR condition of the block filter bank is less restrictive than that of the usual FIR filter banks. The PR condition is expressed in terms of DFT of the analysis filters for convenience of the filter design.

Multiplexing is a technique for dividing a single transmission channel into a number of virtual subchannels. The present paper introduces a new multiplexing system for discrete-time signals based on a polynomial factorization. In this multiplexing system, a linear-filter additive-noise channel is decomposed into independent subchannels that are also modeled as linear-filter additive-noise channels. A configuration and an analysis of the multiplexing system as applied to mobile communications are described in detail, based on a specific selection of polynomial factorization. Multicarrier code-division multiple access (MC-CDMA) is receiving much attention in the field of mobile communications because of its time and frequency diversity property. As is the case with MC-CDMA, in the proposed multiplexing system, the subchannel information is dispersed uniformly in both frequency and time so that degradation localized in frequency or time average out over the subchannels. The averaging has the effect of decreasing the total error probability of transmission. Unlike MC-CDMA however, the multiplexing system creates multiple carriers simply by up-sampling a single complex sinusoidal carrier for each subchannel user. Because of the simple mechanism, the implementation cost is less than that of MC-CDMA.

This paper introduces a generalized cyclic convolution which can be implemented via the conventional cyclic convolution system by the discrete Fourier transform (DFT) with pre-multiplication for the input and post-multiplication for the output. The generalized cyclic convolution is applied for computing a negacyclic convolution. Comparison shows that the proposed implementation is more efficient and simpler in structure than other methods. The generalized cyclic convolution is also applied for the linear convolution by the modified Fermat number transform.

This paper introduces a new recursive factorization of the polynomial, 1-z/sup N/, over the real numbers when N is an even composite integer. The recursive factorization is applied for efficient computation of the discrete Fourier transform (DFT) and the cyclic convolution of real sequences with highly composite even length.

Classes of codes for a multichannel communication system are considered. A fast algorithm is developed to calculate syndromes of multichannel linear systematic codes, including both block and convolutional codes, by using a direct sum of Galois fields.

Recursive filter design techniques are described and developed for finite impulse filters using finite field arithmetic. The finite fields considered have the formGF(q^{2}), the Galois field ofq^{2}elements, and are analogous to the field of complex numbers whenqis a prime such that(-1)is not a quadratic residue. These filters can be designed to yield either a desired finite impulse or finite frequency response function. This filtering technique has other possible applications, including the encoding or decoding of information and signal design. Infinite signal trains can be decomposed naturally into orthogonal sequences which may be useful in the encoding and decoding process and may provide another approach to convolutional coding. Since the recursive filters developed here do not have the accumulation of round-off or truncation error that one might expect in recursive computations, such filters are noise-free transducers in the sense of Shannon.

Encoding and decoding algorithms for Reed-Solomon codes based on Fourier-like transforms on finite field and finite rings are discussed. Classes of codes are proposed for two different types of multiple-user communication systems: a multichannel communication system and a multiaccess communication system. For the first system, a fast decoding algorithm is developed that uses transforms on a finite ring which is isomorphic to a direct sum of Galois fields. For the second system, an efficient (in terms of information rate) coding scheme is proposed which utilizes a direct sum of Galois fields.