On nonassembly in the optimal dimensional synthesis of planar mechanisms

This paper presents a general method for treating nonassembly in the optimal synthesis of planar mechanisms. The synthesis is performed with gradient based optimization algorithms and the sensitivities are calculated analytically through the method of direct differentiation. The analysis is based on the well-established and general method of computational kinematics. In this study the residuals of the joint constraint equations are minimized rather than equated to zero. This makes it possible to perform the kinematic analysis for any proposed design even though it may not be possible to assemble the mechanism. Several examples are provided. Received July 25, 2000     

Optimal design of flexible mechanisms using a parametric approach

In this paper, an effort to develop a more generic design procedure for flexible mechanisms is initiated. Based on a parametric study, the important parameters which affect the stress, displacement, and natural frequency can be closely related. An approach using these relations to obtain the optimal design of flexible mechanisms subject to stress, displacement and natural frequency constraints is presented. Optimality conditions are derived to moderate the conflicting constraints, and a recursion approach is developed to show the application of this study. Two examples using this approach to design flexible mechanisms are presented to demonstrate the idea.     

Controller synthesis via the 4-polynomial approach

In some recent work it was shown that to stabilize systems with real parameter uncertainty it suffices to find a controller that simultaneously stabilizes a finite number of polynomials. These polynomials include those generated from the ‘vertex’ plants as well as some generated by some ‘fictitious’ vertex plants that involve the controller. This paper deals with the issues of existence of such a controller, controller synthesis, and conservativeness of the design. It is shown how this approach can ‘enhance’ the stability robustness of an H_∞ design.     

Graphic simulation of planar dynamic mechanisms

This paper describes the development of easy interactive input and graphic output for a “self-formulating” program, PLANET III, developed at the University of Waterloo. Using the vector-network model, which is a combination of the concepts of vector calculus and linear graph theory, this computer program simulates planar dynamic mechanisms. It is “self-formulating”, because it gives the illusion that the program formulates the equations of motion of the system to be simulated, thus relieving the user of this task. PLANET III can formulate and integrate the equations of motion of multirigid-body, two-dimensional systems when supplied with only the system topology and element characteristics. The versatile graphic output can show both the simulated motion of the system topology and graphs of the position, velocity, acceleration (for masses only) and forces for any system element versus any other system element or time. This permits large quantities of data to be comprehended quickly and easily. The entire process, from data input through graphic output, may be completed generally within a matter of minutes, thereby greatly reducing the time required for each design iteration. Two simulation examples illustrate the practical application of the program.     

Analysis and synthesis of nonlinear time-delay systems via fuzzycontrol approach

Takagi-Sugeno (TS) fuzzy models (1985, 1992) can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete-time nonlinear systems with time delay. The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach. We also present a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities. An illustrative example based on the CSTR model is given to design a fuzzy controller     

Optimal traffic control synthesis for an isolated intersection

A continuous dynamical model of a simplified controlled isolated intersection is derived in order to find and analyze an optimal control policy to minimize total delay. An analytical solution of the optimal control problem with constrained signal light control is presented. The optimal synthesis is found for the four principal control constraint cases. Previous results from the 1960s and 70s are discussed.     

Cranking planar mechanisms on a microcomputer

This paper presents a new method for analyzing the motion of planar mechanisms with an arbitrary number of members and degrees of freedom. This method uses the complex vector notation introduced by Raven to derive the kinematic equations for the position, the velocity and the acceleration of the whole mechanism in matrix form. These matrix equations have m× n dimensions for a mechanism with m members and n joints and are solved by the Gauss-Jordan reduction method. The solution determines the velocity and the acceleration of the joints, and the angular velocity and acceleration of the members. These quantities are subsequently used to generate the new position of the mechanism after a time interval Δt. This approach also permits a direct generation of coupler curves. The simplicity of the method allows the use of small scale desktop computers with a CRT or plotter graphics capability for the illustration of the results. This feature makes the method especially attractive for design and educational purposes.     

Optimal exponential feedback stabilization of planar systems

This paper solves the problem of finding an optimal feedback control ensuring the maximal rate of convergence of system solutions to the origin for a general class of planar control systems including switched, bilinear systems and ones described by differential inclusions, etc. The prescribed control set is assumed to be compact but not necessarily convex. The developed approach is based on finding the minimal Lyapunov exponent of the system with an open loop control which provides an upper bound for the optimal convergence rate of the closed loop system. Then an optimal feedback controller is constructed for which the obtained bound is attained.     

Depth compression via planar segmentation

Augmented Reality applications are set to revolutionize the smartphone industry due to the integration of RGB-D sensors into mobile devices. Given the large number of smartphone users, efficient storage and transmission of RGB-D data is of paramount interest to the research community. While there exist Video Coding Standards such as HEVC and H.264/AVC for compression of RGB/texture component, the coding of depth data is still an area of active research. This paper presents a method for coding depth videos, captured from mobile RGB-D sensors, by planar segmentation. The segmentation algorithm is based on Markov Random Field assumptions on depth data and solved using Graph Cuts. While all prior works based on this approach remain restricted to images only and under noise-free conditions, this paper presents an efficient solution to planar segmentation in noisy depth videos. Also presented is a unique method to encode depth based on its segmented planar representation. Experiments on depth captured from a noisy sensor (Microsoft Kinect) shows superior Rate-Distortion performance over the 3D extension of HEVC codec.

     

Optimal controller synthesis for a class of LTI systems via switched feedback

We develop a switched feedback controller that optimizes the rate of convergence of the state trajectories to the origin for a class of second order LTI systems. Specifically, we derive an algorithm which optimizes the rate of convergence by employing a controller that switches between symmetric gains. As a byproduct of our investigation, we find that, in general, the controllers which optimize the rate of convergence switch between two linear subsystems, one of which is unstable. The algorithm we investigate will design optimal switching laws for the specific case of second order LTI plants of relative degree two.     

Dynamics analysis of linear elastic planar mechanisms

This paper presents a formulation for the dynamics analysis of an elastic mechanism and integrating a stiff system using efficient numerical methods. Because all the elastic degrees of freedom are included in the vector of generalized variables, the size of the equations is much larger than that obtained using either the assumed mode or the distributed parameter finite element approach. However, the resulting system matrix is sparse and the elastic coordinates are absent from the system matrix, and these are useful properties for subsequent numerical analysis. Techniques for solving a system of linear time-variant equations are applied to the dynamics equations, assuming that the system matrix is slow-changing, and thus, may be approximated by a series of piecewise constant matrices. It is argued that the problem of determining the integration time step is transformed into the problem of computing the exponential of the system matrix with automatic time scaling. A numerical example is given to show that the behavior of the rigid coordinates converges to that of an all-rigid-body model by artificially increasing the Young’s modulus of the elastic components, despite the very-high-frequency vibrations of the elastic coordinates induced by the increment of the stiffness.     

Structural design of planar mechanisms with dyads

In this paper, the structural synthesis of planar mechanisms with one, two and three dyads is studied. First a new classification of dyads is introduced and then a new way of constructing mechanisms is explained. The scheme provides a consistent coding scheme for planar mechanisms. The advantage of the classification of a system lies in its simplicity. The solution of the whole system can then be obtained by composing partial solutions. This approach will eliminate the need of storing complete mechanism information in a large database.     

基于平面区域跟踪的目标位姿参数自动测量

提出一种从序列图像中自动跟踪测量目标位置和姿态参数的方法。利用单应性原理和上一帧图像中目标位姿参数的测量结果,将目标上的典型平面区域重建为同时含有几何信息和亮度信息的平面区域模板;然后根据投影方程,将该模板在一定的位置姿态参数下进行投影仿真成像,当模板的仿真成像结果与当前帧图像中的该平面区域达到最佳匹配时,认为此时仿真成像的位置姿态参数即为当前帧图像的测量结果。通过对该匹配问题进行最优化建模和求解,实现了序列图像中目标位姿参数的自动测量。实验结果表明,本文方法能够在序列图像中对含有典型平面区域的目标实现较高精度的自动跟踪测量。     

Optimal remapping in dynamic bulk synchronous computations via a stochastic control approach

A bulk synchronous computation proceeds in phases that are separated by barrier synchronization. For dynamic bulk synchronous computations that exhibit varying phase-wise computational requirements, remapping at runtime is an effective approach to ensure parallel efficiency. The paper introduces a novel remapping strategy for computations whose workload changes can be modeled as a Markov chain. The use of a Markovian model allows us to treat statistical dependence and more complex structure than the usual independent identically distributed random variable assumptions. Our models are quite general and we do not need to impose conditions on the dynamics of the underlying process other than the transition probability matrix. It is shown that optimal remapping can be formulated as a binary decision process: remap or not at a given synchronizing instant. The optimal strategy is then developed for long lasting computations by employing optimal stopping rules in a stochastic control framework. The existence of optimal controls is established. Necessary and sufficient conditions for the optimality are obtained. Furthermore, a policy iteration algorithm is devised to reduce computational complexity and enhance fast convergence to the desired optimal control.     

Optimal occlusion of teeth using planar structure information

In orthodontics, occlusion is defined as the relationship between the upper and lower sets of teeth when the jaws are brought together. Understanding the nature of occlusion has important significance for the diagnosis and treatment of occlusal dysfunction and for planning reconstructive dentistry. The materials of study are 31 pairs of manually aligned dental study models. The upper and lower models are independently digitized using a laser surface scanner. Occlusion can be recovered by detecting and aligning a set of planes on the models. We describe a two-step procedure for determining the occlusal relationship using digitized dental models. The first step is a coarse alignment using four planar structures that are detected by K-means clustering, followed by principal component analysis. The second step is a refinement process using a variant of the iterative closest point technique. The quantitative results show that the algorithm is accurate, with an average measurement discrepancy of 0.74 mm between the physical and virtual models.     

Dynamic balancing of planar mechanisms using toric geometry

A mechanism is statically balanced if for any motion, it does not apply forces on the base. Moreover, if it does not apply torques on the base, the mechanism is said to be dynamically balanced. In this paper, a new method for determining the complete set of dynamically balanced planar four-bar mechanisms is presented. Using complex variables to model the kinematics of the mechanism, the static and dynamic balancing constraints are written as algebraic equations over complex variables and joint angular velocities. After elimination of the joint angular velocity variables, the problem is formulated as a problem of factorization of Laurent polynomials. Using tools from toric geometry including toric polynomial division, necessary and sufficient conditions for static and dynamic balancing of planar four-bar mechanisms are derived.