Fast multipole networks

Two prerequisites for robotic multiagent systems are mobility and communication. Fast multipole networks (FMNs) enable both ends within a unified framework. FMNs can be organized very efficiently in a distributed way from local information and are ideally suited for motion planning using artificial potentials. We compare FMNs to conventional communication topologies, and find that FMNs offer competitive communication performance (including higher network efficiency per edge at marginal energy cost) in addition to advantages for mobility

Assistive trajectories for human-in-the-loop mobile robotic platforms

Autonomous and semi-autonomous smoothly interruptible trajectories are developed which are highly suitable for application in tele-operated mobile robots, operator on-board military mobile ground platforms, and other mobility assistance platforms. These trajectories will allow a navigational system to provide assistance to the operator in the loop, for purpose built robots or remotely operated platforms. This will allow the platform to function well beyond the line-of-sight of the operator, enabling remote operation inside a building, surveillance, or advanced observations whilst keeping the operator in a safe location. In addition, on-board operators can be assisted to navigate without collision when distracted, or under-fire, or when physically disabled by injury

Hybrid and Oriented Harmonic Potentials for Safe Task Execution in Unknown Environment

Harmonic potentials provide globally convergent potential fields that are provably free of local minima. Due to its analytical format, it is particularly suitable for generating safe and reliable robot navigation policies. However, for complex environments that consist of a large number of overlapping non-sphere obstacles, the computation of associated transformation functions can be tedious. This becomes more apparent when: (i) the workspace is initially unknown and the underlying potential fields are updated constantly as the robot explores it; (ii) the high-level mission consists of sequential navigation tasks among numerous regions, requiring the robot to switch between different potentials. Thus, this work proposes an efficient and automated scheme to construct harmonic potentials incrementally online as guided by the task automaton. A novel two-layer harmonic tree (HT) structure is introduced that facilitates the hybrid combination of oriented search algorithms for task planning and harmonic-based navigation controllers for non-holonomic robots. Both layers are adapted efficiently and jointly during online execution to reflect the actual feasibility and cost of navigation within the updated workspace. Global safety and convergence are ensured both for the high-level task plan and the low-level robot trajectory. Known issues such as oscillation or long-detours for purely potential-based methods and sharp-turns or high computation complexity for purely search-based methods are prevented. Extensive numerical simulation and hardware experiments are conducted against several strong baselines.Comment: 16 pages, 13 figure

Solving the potential field local minimum problem using internal agent states

We propose a new, extended artificial potential field method, which uses dynamic internal agent states. The internal states are modelled as a dynamical system of coupled first order differential equations that manipulate the potential field in which the agent is situated. The internal state dynamics are forced by the interaction of the agent with the external environment. Local equilibria in the potential field are then manipulated by the internal states and transformed from stable equilibria to unstable equilibria, allowiong escape from local minima in the potential field. This new methodology successfully solves reactive path planning problems, such as a complex maze with multiple local minima, which cannot be solved using conventional static potential fields

Optimal Navigation Functions for Nonlinear Stochastic Systems

This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential equation. This approach allows for optimality criteria to be incorporated into the navigation function, and generalizes several existing results in navigation functions. It is shown that the HJB and that existing navigation functions in the literature sit on ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. In particular, it is shown that under certain criteria the optimal navigation function is related to Laplace's equation, previously used in the literature, through an exponential transform. Further, analytical solutions to the HJB are available in simplified domains, yielding guidance towards optimality for approximation schemes. Examples are used to illustrate the role that noise, and optimality can potentially play in navigation system design.Comment: Accepted to IROS 2014. 8 Page

Applications of parallel computing in robotics problems

"December 2013.""A Thesis presented to the Faculty of the Graduate School University of Missouri In Partial Fulfillment Of the Requirements for the Degree Master of Science."Thesis advisor: Dr. Guilherme N. DeSouza.Many typical robotics problems involve search in high-dimensional spaces, where real-time execution is hard to be achieved. This thesis presents two case studies of parallel computation in such robotics problems. More specifically, two problems of motion planning-the Inverse Kinematics of robotic manipulators and Path Planning for mobile robots-are investigated and the contributions of parallel algorithms are highlighted. For the Inverse Kinematics problem, a novel and fast solution is proposed for general serial manipulators. This new approach relies on the computation of multiple (parallel) numerical estimations of the inverse Jacobian while it selects the current best path to the desire con- figuration of the end-effector. Unlike other iterative methods, our method converges very quickly, achieving sub-millimeter accuracy in 20.48ms in average. We demonstrate such high accuracy and the real-time performance of our method by testing it with six different robots, at both non-singular and singular configurations, including a 7-DoF redundant robot. The algorithm is implemented in C/C++ using a configurable number of POSIX threads, and it can be easily expanded to use many-core GPUs. For the Path Planning problem, a solution to the problem of smooth path planning for mobile robots in dynamic and unknown environments is presented. A novel concept of Time-Warped Grids is introduced to predict the pose of obstacles on a grid-based map and avoid collisions. The algorithm is implemented using C/C++ and the CUDA programming environment, and combines stochastic estimation (Kalman filter), Harmonic Potential Fields and a Rubber Band model, and it translates naturally into the parallel paradigm of GPU programing. The proposed method was tested using several simulation scenarios for the Pioneer P3- DX robot, which demonstrated the robustness of the algorithm by finding the optimum path in terms of smoothness, distance, and collision-free either in static or dynamic environments, even with a very large number of obstacles.Includes bibliographical references (pages 70-78)

Robotic Motion using Harmonic Functions and Finite Elements

The harmonic functions have proved to be a powerful technique for motion planning in a known environment. They have two important properties: given an initial point and an objective in a connected domain, a unique path exists between those points. This path is the maximum gradient path of the harmonic function that begins in the initial point and ends in the goal point. The second property is that the harmonic function cannot have local minima in the interior of the domain (the objective point is considered as a border). This paper proposes a new method to solve Laplace's equation. The harmonic function solution with mixed boundary conditions provides paths that verify the smoothness and safety considerations required for mobile robot path planning. The proposed approach uses the Finite Elements Method to solve Laplace's equation, and this allows us to deal with complicated shapes of obstacles and walls. Mixed boundary conditions are applied to the harmonic function to improve the quality of the trajectories. In this way, the trajectories are smooth, avoiding the corners of walls and obstacles, and the potential slope is not too small, avoiding the difficulty of the numerical calculus of the trajectory. Results show that this method is able to deal with moving obstacles, and even for non-holonomic vehicles. The proposed method can be generalized to 3D or more dimensions and it can be used to move robot manipulators