Series-parallel six-element synthesis of biquadratic impedances

The object of this paper is to give a complete treatment of the realizability of positive-real biquadratic impedance functions by six-element series-parallel networks comprising resistors, capacitors, and inductors. This question was studied but not fully resolved in the classical electrical circuit literature. Renewed interest in this question arises in the synthesis of passive mechanical impedances. Recent work by the authors has introduced the concept of a regular positive-real functions. It was shown that five-element networks are capable of realizing all regular and some (but not all) nonregular biquadratic positive-real functions. Accordingly, the focus of this paper is on the realizability of nonregular biquadratics. It will be shown that the only six-element series-parallel networks which are capable of realizing nonregular biquadratic impedances are those with three reactive elements or four reactive elements. We identify a set of networks that can realize all the nonregular biquadratic functions for each of the two cases. The realizability conditions for the networks are expressed in terms of a canonical form for biquadratics. The nonregular realizable region for each of the networks is explicitly characterized. © 2004-2012 IEEE.

A six sensor method for measuring acoustic properties in ducts.

An accurate description of sound propagation in a duct is important to obtain the sound power radiating from a source in both near and far fields. A technique has been developed and applied to decompose higher-order modes of sound emitted into a duct. Traditional experiments and theory based on two-sensor methods are limited to the plane-wave contribution to the sound field at low frequency. Due to the increase in independent measurements required, a computational method has been developed to simulate sensitivities of real measurements (e.g., noise) and optimize the set-up. An experimental rig has been constructed to decompose the first two modes using six independent measurements from surface, flush-mounted microphones. Experiments were initially performed using a loudspeaker as the source for validation. Subsequently, the sound emitted by a mixed-flow fan has been investigated and compared to measurements made in accordance with the internationally standardized in-duct fan measurement method. This method utilizes large anechoic terminations and a procedure involving averaging over measurements in space and time to account for the contribution from higher-order modes. The new method does not require either of these added complications and gives detail about the underlying modal content of the emitted sound.

Learning legged locomotion

Legged locomotion of biological systems can be viewed as a self-organizing process of highly complex system-environment interactions. Walking behavior is, for example, generated from the interactions between many mechanical components (e.g., physical interactions between feet and ground, skeletons and muscle-tendon systems), and distributed informational processes (e.g., sensory information processing, sensory-motor control in central nervous system, and reflexes) [21]. An interesting aspect of legged locomotion study lies in the fact that there are multiple levels of self-organization processes (at the levels of mechanical dynamics, sensory-motor control, and learning). Previously, the self-organization of mechanical dynamics was nicely demonstrated by the so-called Passive Dynamic Walkers (PDWs; [18]). The PDW is a purely mechanical structure consisting of body, thigh, and shank limbs that are connected by passive joints. When placed on a shallow slope, it exhibits natural bipedal walking dynamics by converting potential to kinetic energy without any actuation. An important contribution of these case studies is that, if designed properly, mechanical dynamics can generate a relatively complex locomotion dynamics, on the one hand, and the mechanical dynamics induces self-stability against small disturbances without any explicit control of motors, on the other. The basic principle of the mechanical self-stability appears to be fairly general that there are several different physics models that exhibit similar characteristics in different kinds of behaviors (e.g., hopping, running, and swimming; [2, 4, 9, 16, 19]), and a number of robotic platforms have been developed based on them [1, 8, 13, 22]. © 2009 Springer London.

Motor control optimization of compliant one-legged locomotion in rough terrain

While underactuated robotic systems are capable of energy efficient and rapid dynamic behavior, we still do not fully understand how body dynamics can be actively used for adaptive behavior in complex unstructured environment. In particular, we can expect that the robotic systems could achieve high maneuverability by flexibly storing and releasing energy through the motor control of the physical interaction between the body and the environment. This paper presents a minimalistic optimization strategy of motor control policy for underactuated legged robotic systems. Based on a reinforcement learning algorithm, we propose an optimization scheme, with which the robot can exploit passive elasticity for hopping forward while maintaining the stability of locomotion process in the environment with a series of large changes of ground surface. We show a case study of a simple one-legged robot which consists of a servomotor and a passive elastic joint. The dynamics and learning performance of the robot model are tested in simulation, and then transferred the results to the real-world robot. ©2007 IEEE.

One-legged locomotion with a compliant passive joint

There is an increasing attention of exploiting compliant materials for the purpose of legged locomotion, because they provide significant advantages in locomotion performance with respect to energy efficiency and stability. Toward establishing a fundamental basis for this line of research, a minimalistic locomotion model of a single legged system is explored in this paper. By analyzing the dynamic behavior of the system in simulation and a physical robotic platform, it is shown that a stable locomotion process can be achieved without the necessity of sensory feedback. In addition, further analysis characterizes the relation between motor control and the natural body dynamics determined by morphological properties such as body mass and spring constant. © 2006 The authors.

Finding resonance: Adaptive frequency oscillators for dynamic legged locomotion

There is much to gain from providing walking machines with passive dynamics, e.g. by including compliant elements in the structure. These elements can offer interesting properties such as self-stabilization, energy efficiency and simplified control. However, there is still no general design strategy for such robots and their controllers. In particular, the calibration of control parameters is often complicated because of the highly nonlinear behavior of the interactions between passive components and the environment. In this article, we propose an approach in which the calibration of a key parameter of a walking controller, namely its intrinsic frequency, is done automatically. The approach uses adaptive frequency oscillators to automatically tune the intrinsic frequency of the oscillators to the resonant frequency of a compliant quadruped robot The tuning goes beyond simple synchronization and the learned frequency stays in the controller when the robot is put to halt. The controller is model free, robust and simple. Results are presented illustrating how the controller can robustly tune itself to the robot, as well as readapt when the mass of the robot is changed. We also provide an analysis of the convergence of the frequency adaptation for a linearized plant, and show how that analysis is useful for determining which type of sensory feedback must be used for stable convergence. This approach is expected to explain some aspects of developmental processes in biological and artificial adaptive systems that "develop" through the embodied system-environment interactions. © 2006 IEEE.