Angle rigidity and its usage to stabilize multi-agent formations in 2D

Motivated by the challenging formation stabilization problem for mobile robotic teams wherein no distance or relative position measurements are available but each robot can only measure some of relative angles with respect to its neighbors in its local coordinate frame, we develop the notion of "angle rigidity" for a multi-point framework, named "angularity", consisting of a set of nodes embedded in a Euclidean space and a set of angle constraints among them. Different from bearings or angles defined in a global frame, the angles we use do not rely on the knowledge of a global frame and are signed according to the counter-clockwise direction. Here angle rigidity refers to the property specifying that under proper angle constraints, the angularity can only translate, rotate or scale as a whole when one or more of its nodes are perturbed locally. We first demonstrate that this angle rigidity property, in sharp comparison to bearing rigidity or other reported rigidity related to angles of frameworks in the literature, is not a global property since an angle rigid angularity may allow flex ambiguity. We then construct necessary and sufficient condit

Bearing rigidity and formation stabilization for multiple rigid bodies in SE(3)

In this work, we first distinguish different notions related to bearing rigidity in graph theory and then further investigate the formation stabilization problem for multiple rigid bodies. Different from many previous works on formation control using bearing rigidity, we do not require the use of a shared global coordinate system, which is enabled by extending bearing rigidity theory to multi-agent frameworks embedded in the three dimensional special Euclidean group SE(3) and expressing the needed bearing information in each agent's local coordinate system. Here, each agent is modeled by a rigid body with 3 DOFs in translation and 3 DOFs in rotation. One key step in our approach is to define the bearing rigidity matrix in SE(3) and construct the necessary and sufficient conditions for infinitesimal bearing rigidity. In the end, a gradient-based bearing formation control algorithm is proposed to stabilize formations of multiple rigid bodies in SE(3)

Stabilizing a mobile agent under two angle constraints

Recently, angle-based formation control laws have been proposed assuming that each agent only aims at maintaining one desired angle with respect to its neighbors. To extend the angle-based formation control algorithms to more general cases, we propose for each agent to maintain simultaneously multiple prescribed angles. As a first step, we investigate how an agent can be enabled to maintain two desired angles taking three static and collinear markers as references. We first show the condition for the existence of such positions for any given two angle constraints. Then, we propose a formation control law that uses local bearing measurements with respect to the markers, under which the local convergence of the moving agent to the desired position is guaranteed while satisfying the two constraints of the desired angles. A simulation example is provided to demonstrate the correctness of the theoretical results

Adaptive Regularized Level Set Method for Weak Boundary Object Segmentation

An adaptive regularized level set method for image segmentation is proposed. A weighted p(x)-Dirichlet integral is presented as a geometric regularization on zero level curve, which is used to diminish the influence of image noise on level set evolution while ensuring the active contours not to pass through weak object boundaries. The idea behind the new energy integral is that the amount of regularization on the zero level curve can be adjusted automatically by the variable exponent p(x) to fit the image data. This energy is then incorporated into a level set formulation with an external energy term that drives the motion of the zero level set toward the desired objects boundaries, and a level set function regularization term that is necessary for maintaining stable level set evolution. The proposed model has been applied to a wide range of both real and synthetic images with promising results

Angle-based formation shape control with velocity alignment

With the rapid development of sensor technology, bearing/angle measurements are becoming cheaper and more reliable, which motivates the study of angle-based formation shape control. This work studies how to achieve angle-based formation control and velocity alignment at the same time, in which all agents can form a desired angle-rigid formation and translate with the same velocity simultaneously. The agents' communication topology for the achievement of velocity alignment is described by a connected graph, while the formation shape is determined by a set of angles that are associated with triangles within the formation and computed using bearing measurements. A simulation example validates the effectiveness of the theoretical results.</p

State filtering and parameter estimation for two input two output systems with time delay

This paper focuses on presenting a new identification algorithm to estimate the parameters and state variables for two-input two-output dynamic systems with time delay based on canonical state space models. First, the related input-output equation is determined and transformed into an identification oriented model, which does not involve in the unmeasurable states, and then a residual based least squares identification algorithm is presented for the estimations. After the parameters being estimated, the system states are subsequently estimated by using the estimated parameters. Through theoretical analysis, the convergence of the algorithm is derived to provide assurance for applicability. Finally, a selected simulation example is given for a meaningful case study to show the effectiveness of the proposed algorithm

Ionic liquid-assisted synthesis of Yb3+-Tm3+ codoped Y7O6F9 petal shaped microcrystals with enhanced upconversion emission

Petal-like Yb3+-Tm3+ codoped Y7O6F9 microparticles were achieved via ionic liquid-assisted (IL) hydrothermal process. The emission efficiency of Y7O6F9:Yb3+/Tm3+ powders is much stronger than that of Y2O3:Yb3+/Tm3+ sample. Under excitation at 980 nm with an unfocused laser beam under weak pump density of ∼0.1 W/cm2 (pump power 10 mW), the UC emission of the sample can been seen clearly. Four emission bands at 477, 540, 647 and 692 nm are observed and correspond to the 1G4 state to 3H6 state, 1D2 state to 3H5 state, 1G4 sate to 3F4 state, and 3F3 state to 3H6 state transition of Tm3+ ions. The enhanced UC emission is related to high crystallinity and lower effective phonon energy of oxyfluorides. The ionic liquid (IL) of [BMIM][BF4] is used both as the reaction medium and the source of F−

Unified Multi-Objective Genetic Algorithm for Energy Efficient Job Shop Scheduling

In recent years, people have paid more and more attention to traditional manufacturing’s environmental impact, especially in terms of energy consumption and related emissions of carbon dioxide. Except for adopting new equipment, production scheduling could play an important role in reducing the total energy consumption of a manufacturing plant. Machine tools waste a considerable amount of energy because of their underutilization. Consequently, energy saving can be achieved by switching machines to standby or off when they lay idle for a comparatively long period. Herein, we first introduce the objectives of minimizing non-processing energy consumption, total weighted tardiness and earliness, and makespan into a typical production scheduling model-the job shop scheduling problem, based on a machine status switching framework. The multi-objective genetic algorithm U-NSGA-III combined with MME (a heuristic algorithm combined with the MinMax (MM) and Nawaz–Enscore–Ham (NEH) algorithms) population initialization method is used to solve the problem. The multi-objective optimization algorithm can generate a Pareto set of solutions so that production managers can flexibly select a schedule from these non-dominated schedules based on their priorities. Three sets of numerical experiments have been carried out on the extended Taillard benchmark to verify this three-objective model’s effectiveness and the multi-objective optimization algorithm. The results show that U-NSGA-III has obtained better Pareto solutions in most test problem instances than NSGA-II and NSGA-III. Furthermore, the non-processing energy consumption is reduced by 46%-69%, which is 13-83% of the total energy consumption