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In this paper, the problem of motion planning for parallel robots in the presence of static and dynamic obstacles has been investigated. The proposed algorithm can be regarded as a synergy of convex optimization with discrete optimization and receding horizon. This algorithm has several advantages, including absence of trapping in local optimums and a high computational speed. This problem has been fully analyzed for two three-DOF parallel robots, ie 3s-RPR parallel mechanism and the so-called Tripteron, while the shortest path is selected as the objective function. It should be noted that the first case study is a parallel mechanism with complex singularity loci expression from a convex optimization problem standpoint, while the second case is a parallel manipulator for which each limb has two links, an issue which increases the complexity of the optimization problem. Since some of the constraints are non-convex, two approaches are introduced in order to convexify them: (1) A McCormick-based relaxation merged with a branch-and-prune algorithm to prevent it from becoming too loose and (2) a first-order approximation which linearizes the non-convex quadratic constraints. The computational time for the approaches presented in this paper is considerably low, which will pave the way for online applications. [ABSTRACT FROM PUBLISHER]

Most algorithms in probabilistic sampling-based path planning compute collision-free paths made of straight line segments lying in the configuration space. Due to the randomness of sampling, the paths make detours that need to be optimized. The contribution of this paper is to propose a basic gradient-based algorithm that transforms a polygonal collision-free path into a shorter one. While requiring only collision checking, and not any time-consuming obstacle distance computation nor geometry simplification, we constrain only part of the configuration variables that may cause a collision, and not entire configurations. Thus, parasite motions that are not useful for the problem resolution are reduced without any assumption. Experimental results include navigation and manipulation tasks, eg a manipulator arm-filling boxes and a PR2 robot working in a kitchen environment. Comparisons with a random shortcut optimizer and a partial shortcut have also been studied. [ABSTRACT FROM PUBLISHER]

We discuss the effective implementation of parallel processing for linear prediction-based uniform state sampling (LPUSS). In previous work, we proposed LPUSS as an optimization algorithm for mechanical motions that assures high optimality of the solutions and computational efficiency. In parallel computation, LPUSS requires balanced memory allocation and managed processing timing. In this paper, we propose an effective parallel computing method that assures high optimality and calculation efficiency in parallel processing using GPU processor. We conducted two experiments to validate the proposed method. In the first experiment, we compared single-thread processing for LPUSS and the proposed parallel processing. As a result of this experiment, calculation speed of LPUSS was about 4–20 times faster than that with single-thread CPU. In the second experiment, we applied the proposed method to the optimization of sixtuple inverted pendulum. As a result, the proposed method optimized the motion within 40 minutes. According to our survey, there is no other optimization method that is applicable to higher than quadruple inverted pendulum models with standard constraints. [ABSTRACT FROM AUTHOR]

In this paper we address the problem of finding time-optimal search paths in known environments. In particular, we address the problem of searching a known environment for an object whose unknown location is characterized by a known probability density function (PDF). With this formulation, the time required to find the object is a random variable induced by the choice of search path together with the PDF for the object's location. The optimization problem we consider is that of finding the path that minimizes the expected value of the time required to find the object. As the complexity of the problem precludes finding an exact optimal solution, we propose a two-level, heuristic approach to finding the optimal search path. At the top level, we use a decomposition of the workspace based on critical curves to impose a qualitative structure on the solution trajectory. At the lower level, individual segments of this trajectory are refined using local numerical optimization methods. We have implemented the algorithm and present simulation results for the particular case when the object's location is specified by the uniform PDF. [ABSTRACT FROM AUTHOR]

Currently, third-party logistics (3PL) services are growing rapidly. In the current business climate, the goal of each 3PL firm is to reduce the time required for warehouse design. In this paper, a warehouse design problem is discussed. The problem is to determine the number of machines used in a warehouse and the product flow among the devices. In the conventional design process, such a problem would be solved with experimental and intuitional approaches. However, conventional approaches require large amounts of time. In addition, the design outcome is dependent on the skill of the designer. In order to provide theoretical guidelines for the design itself and shorten the design process, we propose a new design method using an extended network flow model. The network flows are expressed as the combination of the flow in the preparation time and that in the lead time. The mathematical model is constructed and solved as a threshold optimization algorithm including the mixed integer linear programming problem. We then evaluated the feasibility of the proposed model and method using real data, and confirmed the effect of the proposed method with regard to time reduction and the obtained design results. [ABSTRACT FROM AUTHOR]