An approach to solving continuous global optimization problems was developed. It builds on two innovative concepts, subenergy tunneling and non-Lipschitzian terminal repellers, to ensure escape from local minima in a fast, reliable, and computationally efficient manner. The generally applicable methodology is embodied in the TRUST (terminal repeller unconstrained subenergy tunneling) algorithm, which is deterministic, scalable, and easy to implement. Benchmark results show that TRUST is faster and more accurate than previously reported global optimization techniques. An application of TRUST to a large-scale exploratory seismology problem of substantial computational complexity (that is, residual statics corrections) is also reported.

An important characteristic of mobile manipulators is their particular kinematic redundancy created by the addition of the degrees of freedom of the platform and those of the manipulator. This kinematic redundancy is very desirable since it allows mobile manipulators to operate under many modes of motion and to perform a wide variety of tasks. On the other hand, it also significantly complicates the problem of planning a series of sequential tasks, in particular for the critical times at which the system needs to "switch" from one task to the other (task commutation), with changes in mode of motion, task requirement, and task constraints. This paper focuses on the problem of planning the positions and configurations in which the system needs to be at task commutation in order to assure that it can properly initiate the next task to be performed. The concept of and need for "commutation configurations" in sequences of mobile manipulator tasks is introduced, and an optimization approach is proposed for their calculation during the task sequence planning phase. A variety of optimization criteria were previously investigated to optimize the task commutation configurations of the system when task requirements involve obstacle avoidance, reach, maneuverability, and optimization of strength. In this paper, we show that a "minimax" approach is particularly adapted for most of these requirements. We develop the corresponding criteria and discuss solution algorithms to solve the "minimax" optimization problems. An implementation of the algorithms for our HERMIES-I11 mobile manipulator is then described and sample results are presented and discussed.

This article addresses the problem of time-optimal motions for a mobile platform in a planar environment. The platform has two nonsteerable, independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories between these configurations, assuming an unobstructed environment. Using Pontryagin's maximum principle (PMP), we formally demonstrate that all time-optimal motions of the platform for this problem occur for bang-bang controls on the wheels (at each instant, the acceleration on each wheel is at either its upper or its lower limit). The PMP, however, provides only the conditions necessary for time optimality. To find the time- optimal robot trajectories, we first parameterize the bang-bang trajectories using the switch times on the wheels (the times at which the wheel accelerations change sign). With this param eterization, we can fully search the robot trajectory space and find the switch times that will produce particular paths to a desired final configuration of the platform. We show numer ically that robot trajectories with three switch times (two on one wheel and one on the other) can reach any position, while trajectories with four switch times can reach any configuration. By numerical comparison with other trajectories involving sim ilar or greater numbers of switch times, we then identify the sets of time-optimal trajectories. These are uniquely defined using ranges of the parameters and consist of subsets of trajec tories with three switch times (for the problem when the final orientation of the robot is not specified) or four switch times (when a full final configuration is specified). We conclude with a description of the use of the method for trajectory planning for one of our robots and discuss some comparisons of sample time-optimal paths with minimum length paths.