Chi-Kuang Hwang

A novel spherical wheel driven by chains with guiding wheels

A novel combination of chains with guiding wheel and spherical wheel unit (CWWU1) is presented in this paper, and its operating principle is basically a spherical wheel driven by two perpendicular pairs of chains with a set of guiding wheels. Thus, a CWWU1 base robot similar to the previous CWWU (combination of Omni wheel and spherical wheel unit) can perform the static and dynamic balancing function that a single wheel with inverse mouse-ball drive developed by Carnegie Mellon University (CMU) can also achieve. However, the previous CWWU has an unwanted compromise in which the strength is inversely proportional to the smoothing motion needed to be made. That is, increase the Omni wheels to improve the smoothness of motion will reduce the spacing of Omni wheel which will weak the strength of the Omni wheels. The CWWU1 can solve this problem, and the major difference between them is that the motion of CWWU1 can be smoother than the previous CWWU due to more than one guiding wheel to contact the surface of the spherical wheel. The other difference is that the size of CWWU1 can be reduced more as compared with the previous CWWU in case of size limit applications. Both robots have several exclusive features which can resolve key problems inherited in the CMU robot. Especially, the simultaneous demand of both a high-friction and low-friction material for the spherical ball is an undesired compromise needed to make for the CMU robot.

A novel spherical wheel driven by Omni wheels

A novel combination of Omni wheel and spherical wheel unit (CWWU) is presented in this paper, and its operating principle is basically a spherical wheel driven by two perpendicular pairs of Omni wheels. Thus, a CWWU base robot can perform the static and dynamic balancing function that a single wheel with inverse mouse-ball drive developed by Carnegie Mellon University (CMU) can achieve. The previous rolling/balancing machines cannot immediately drive in a given direction without first re-orienting the drive mechanism. The major feature of the presented CWWU base robot and the CMU robot is that both of them can move directly in any direction. As compared the Omni wheel base robot with the proposed one, the main drawback of the Omni wheel robot is the cancellation of opposite portion of the driving forces. Moreover, the CWWU base robot has several exclusive features which can resolve some problems inherited in the CMU robot. Especially, the simultaneous demand of both a high-friction and low-friction material for the spherical ball is a compromise needed to make for the CMU robot, but not for the proposed CWWU base robot.

Modeling of a spherical robot driven by Omni wheels

This paper mainly derives the model of the invented spherical robot using Omni wheels to drive a spherical wheel. The dynamical model is derived based on Euler Lagrange approach. The general form of the robot is also presented. It is noted that the control input of the attitude of robot body originally is the torque exerted by two pairs of Omni wheels to drive the spherical wheel, and it can be substituted with the acceleration of the spherical wheel. In other words, the acceleration of the spherical wheel will seriously affect the attitude of the robot body. It implies that the constant speed control of the spherical wheel with zero tilt can be achieved by zero acceleration. The trajectory control of the mobile robot becomes very tough, because a constant speed is not necessary to be a zero speed which is required for a fixing point trajectory control.

Observer base linear quadratic regulation with estimated state feedback control

For the continuous infinite horizon time-invariant linear quadratic regulator problem (LQR), in the paper, the optimal state feedback controller based on the estimated state of the observer can be decoupled by the proposed approach which resulting one continuous time algebraic Riccati equation (CARE) for the controller design and one matrix equality equation (MEE) for the observer design. A coupling term related the CARE of the controller is found to be existed in the MEE of the observer. Unlike the separate principle to design the controller and observer separately without any coupling term, the design of the observer should consider the coupling term related to the CARE of the controller. The coupling problem between the controller and the observer usually exists in the linear matrix inequality (LMI) approach, and it is the main problem to be solved. The two-stage scheme is popular in the LMI approach, and the proposed method is similar to it, but adopting equality instead of inequality.

Time series analysis during the releasing arrow stage

In this paper, during the releasing arrow stage, the relationship between the time series trajectory and the archery performance has been studied. With the aid of the high sampling rate 1200 frames/second of video camera, the time series aiming trajectory during the releasing stage can be captured for analysis, especially the releasing string motion. The linear time invariant auto-regressive exogenous (ARX) process is adopted to model the intended aiming trajectory before the releasing arrow stage. Then based on the model the estimated trajectory during the releasing arrow stage is evaluated as the reference, so its difference between the real one is the main focus in the paper. According to these discrepancies some key parameters are defined first, and the implementation of correlation approach can result in some significant relationships which can characterize his particular releasing string motion during this stage. For example, his releasing arrow trajectory always has an upper linear trend along the vertical direction, and the vertical deviation on the target plays more important role than the radial deviation.

Performance analysis based on an emulated archery machine

An emulated archery machine is designed for eliminating the human motion effect, so the performance analysis related to the various setting of archery individual equipment can be easily conducted and very its effect on the archery performance. The associated specifications of the emulated archery machine considered to be suitable for archery sport are also illustrated in details. The functions of arrow speed and pull forces sensors are also described. Four dissimilar types of vanes have been tested to compare their stability of the arrow speed. Four distinct positions for attaching the vane have also been tried to check their influence on the arrow speed. The effects of various numbers of strings on the arrow speed have also been observed by two different settings. The popularity of the spin-wing vane can be verified by the experimental results such as the fast average arrow speed and high stability associated with this particular vane.

Aiming trajectory analysis based on ARMAX model

In this paper, the linear time invariant auto-regressive moving average exogeneous (ARMAX) process is adopted to model the aiming trajectory. Both of the vertical and the horizontal deviations are studied instead of the radius or score only. The magnitude of associated poles of the auto-regressive part whether slightly greater than one is used to determine the fairness of the proposed model. The exogeneous input is designed to model the adjustment of the deviation between the aiming point and the center of target. In other words, the normal aiming style can be modeled by the combination of these two parts. Afterwards, the moving average part is related to the muscle strength and stability of archers. The mean and variance of the drive noise of the moving average part are also calculated and utilized to justify the correctness of the proposed model. Previous study based on AR2 model can not reveal the importance of the exogeneous input, but in the paper it becomes very significant for the correctness of the proposed model. As expected, there are some similar results. However, some results show that even though the attendants are all expertise in archery, some of their data are so distinct.

An Exact Closed-Form Formula of Collision Probability in Diverse Multiple Access Communication Systems with Frame Slotted Aloha Protocol

Abstract For diverse multiple access communication systems based on frame slotted aloha (FSA) protocol, it is important to analyze collision probability for the system performance evaluation. As shown in the literature, for general settings, it is difficult to derive an exact and closed-form solution for collision probability without approximation. Recently, an exact solution based on generic analytical approach (GAA) [31] has been proposed, yet its numerical computation will become difficult when the number of slots is larger than 16. In this paper, we develop an exact closed-form formula (ECFF) for collision probability that can not only overcome the computational deficiency of GAA in the presence of a large number of slots, but also reduce the computation complexity of collision probability. Surprisingly, by introducing a differentiation operator to form a hybrid recursive equation and applying various algebraic properties of Laplace transform and Z transform, the final collision probability can be represented by a compact double summation. Accuracy of the ECFF and comparison with the GAA have been studied by Monte Carlo simulation.

Cascade sliding mode control of a spherical wheel robot driven by Omni wheels

The target of the paper is a spherical robot using Omni wheels to drive a spherical wheel, and its position control based on the cascade sliding model control (CSMC) has been studied. The structure of the CSMC is cascade combination of states of this dynamic model and a series of sliding surfaces. Because the CSMC is easy to result in a constant speed of spherical wheel, a constant without any switching cascade sliding model control, denoted as CSMCl, has been proposed to solve the undesired constant speed problem. The positive constant coefficients without any switching can release the body convergent rate, so the constant speed problem can be avoided to achieve the position control.