This work makes two contributions to geometric motion planning for multiple robots: i) motion plans can be determined that simultaneously optimize an independent performance criterion for each robot; ii) a general spectrum is defined between decoupled and centralized planning. By considering independent performance criteria, we introduce a form of optimality that is consistent with concepts from multi-objective optimization and game theory research. Previous multiple-robot motion planning approaches that consider optimality combine individual criteria into a single criterion. As a result, these methods can fail to find many potentially useful motion plans. We present implemented, multi-robot motion planning algorithms that are derived from the principle of optimality, for three problem classes along the spectrum between centralized and decoupled planning: i) coordination along fixed, independent paths; ii) coordination along independent roadmaps; iii) general, unconstrained motion planning. Several computed examples are presented for all three problem classes that illustrate the concepts and algorithms.

Optimal motion planning for multiple robots having independent goals

Coordinated Path Planning for Multiple Robots

We propose a distributed and optimal motion planning algorithm for multiple robots. The computationally expensive problem is decomposed into two modules: path planning and velocity planning. The D* search method is applied in both modules, based on either geometric formulation or schedule formulation. Optimization is achieved at the individual robot level by defining cost functions, and also at the team level by a global measurement function reflecting performance indices of interest as a team. Contrary to our knowledge of previous results on multi-robot motion planning that either obtain optimal solutions through centralized and exhaustive computing, or achieve distributed implementations without considering any optimization issues, our approach combines these two features and explicitly optimizes performance functions through a distributed implementation. It is also one of the few that is capable of handling outdoor rough terrain environments and real time replanning. Simulations are shown on a Mars-like rough terrain using a 3D vehicle planner and control simulator. The algorithm was also implemented and successfully run on a group of Nomad 200 indoor robots.

/pdf/a-distributed-and-optimal-motion-planning-approach-for-3c968rxdbp.pdf

A distributed and optimal motion planning approach for multiple mobile robots

Presents a geometry-based approach for multiple mobile robot motion coordination. The problem is to coordinate the motions of several robots moving along fixed independent paths to avoid mutual collisions. The proposed algorithm is based on a bounding box representation of the obstacles in the so-called coordination diagram. The algorithm is resolution-complete but it is shown to be complete for a large class of inputs. Despite the exponential dependency of the coordination problem, the algorithm efficiently solves problems involving up to ten robots in worst-case situations and more than 100 robots in practical ones.

/pdf/path-coordination-for-multiple-mobile-robots-a-resolution-4n7jhugw8q.pdf

Path coordination for multiple mobile robots: a resolution-complete algorithm

This paper focuses on the collision-free coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical programming, consists of identifying collision segments along each robot's path, and then optimizing the robots' velocities along the collision and collision-free segments. First, for each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding two-point boundary value problems. The collision avoidance constraints for pairs of robots can then be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations, which provide schedules that give lower and upper bounds on the optimum; the upper bound schedule is designed to provide continuous velocity trajectories that are feasible. The approach is illustrated with coordination of multiple robots, modeled as double integrators subject to velocity and acceleration constraints. An application to coordination of nonholonomic car-like robots is described, along with implementation results for 12 robots.

https://link.springer.com/content/pdf/10.1007%2F978-3-540-45058-0_14.pdf

Coordinating Multiple Robots with Kinodynamic Constraints Along Specified Paths

A simple time delay method for avoiding collisions between two general robot arms is proposed. Links of the robots are approximated by polyhedra and the danger of collision between two robots is expressed by distance functions defined between the robots. The collision map scheme, which can describe collisions between two robots effectively, is adopted. The minimum delay time value needed for collision avoidance is obtained by a simple procedure of following the boundary contour of collision region on collision map. To demonstrate the effectiveness of the proposed time delay method, a computer simulation study is shown where a collision is likely to occur realistically. >

Collision avoidance of two general robot manipulators by minimum delay time

The prototype of the field emission display with carbon nanotube emitter is developed in this study. The cathode structure is based on the typical top-gate structure, and electron focusing gate and resistive layer are applied. To improve the brightness and color gamut of the prototype, new phosphor material, SrGa2S4: Eu, is adopted instead of conventional CRT-green phosphor. By replacing the green phosphor, the prototype shows significant improvements in the brightness and color gamut. At the anode voltage of 7 kV and the anode current of 2∼3 μA/cm2, the brightness is higher than 600 cm/m2. The luminous efficiency of the prototype is about 7.7 lm/Watt. The images from color video operation of the prototype are shown.

63.1: Invited Paper: Recent Improvements in Brightness and Color Gamut of Carbon Nanotube Field Emission Display

In this study, the field emission display with carbon nanotube emitter is developed for the large size HDTV application. Two structures for electron beam focusing are developed on the typical top-gate cathode. The metal grid and focusing gate structure are proved to be effective for the focusing. The data switching voltage for the double gate structure is lower than 30V which is competitive value in respect of the cost for driver electronics. The brightness and color gamut are comparable to those of the commercial product such as CRT.

53.3: Invited Paper: CNT FEDs for Large Area and HDTV Applications

Disclosed is low-voltage phosphor material having a high level of brightness and a manufacturing method thereof. The phosphor material includes (ZnCd)S or ZnS based compound phosphor material, and a metal added to the phosphor material, the metal having properties for preventing oxidation and reducing surface charge of the phosphor material. The method of manufacturing the phosphor material includes the steps of adding (ZnCd)S based compound phosphor material or ZnS based compound phosphor material to a vehicle and mixing the resulting mixture, and adding a metal to the mixture, the metal having properties for preventing oxidation and reducing surface charge of the phosphor material. Preferably, the metal is Zn having a diameter of 0.1 to 10 μm and a purity of 95%. Also preferably, the metal is 0.01 to 10.0 wt % based on the wt % of the phosphor material.

Cheol Hyeon Chang

Papers

Collision avoidance of two general robot manipulators by minimum delay time

63.1: Invited Paper: Recent Improvements in Brightness and Color Gamut of Carbon Nanotube Field Emission Display

53.3: Invited Paper: CNT FEDs for Large Area and HDTV Applications

Low-voltage phosphor material having a high degree of brightness and a manufacturing method thereof