Practical Distance Functions for Path-Planning in Planar Domains

Path planning is an important problem in robotics. One way to plan a path between two points $x,y$ within a (not necessarily simply-connected) planar domain $\Omega$, is to define a non-negative distance function $d(x,y)$ on $\Omega\times\Omega$ such that following the (descending) gradient of this distance function traces such a path. This presents two equally important challenges: A mathematical challenge -- to define $d$ such that $d(x,y)$ has a single minimum for any fixed $y$ (and this is when $x=y$), since a local minimum is in effect a "dead end", A computational challenge -- to define $d$ such that it may be computed efficiently. In this paper, given a description of $\Omega$, we show how to assign coordinates to each point of $\Omega$ and define a family of distance functions between points using these coordinates, such that both the mathematical and the computational challenges are met. This is done using the concepts of \emph{harmonic measure} and \emph{$f$-divergences}. In practice, path planning is done on a discrete network defined on a finite set of \emph{sites} sampled from $\Omega$, so any method that works well on the continuous domain must be adapted so that it still works well on the discrete domain. Given a set of sites sampled from $\Omega$, we show how to define a network connecting these sites such that a \emph{greedy routing} algorithm (which is the discrete equivalent of continuous gradient descent) based on the distance function mentioned above is guaranteed to generate a path in the network between any two such sites. In many cases, this network is close to a (desirable) planar graph, especially if the set of sites is dense

Vehicle Motion Planning Using Stream Functions

Borrowing a concept from hydrodynamic analysis, this paper presents stream functions which satisfy Laplace's equation as a local-minima free method for producing potential-field based navigation functions in two dimensions. These functions generate smoother paths (i.e. more suited to aircraft-like vehicles) than previous methods. A method is developed for constructing analytic stream functions to produce arbitrary vehicle behaviors while avoiding obstacles, and an exact solution for the case of a single uniformly moving obstacle is presented. The effects of introducing multiple obstacles are discussed and current work in this direction is detailed. Experimental results generated on the Cornell RoboFlag testbed are presented and discussed, as well as related work applying these methods to path planning for unmanned air vehicles

Harmonic Exponential Families on Manifolds

In a range of fields including the geosciences, molecular biology, robotics and computer vision, one encounters problems that involve random variables on manifolds. Currently, there is a lack of flexible probabilistic models on manifolds that are fast and easy to train. We define an extremely flexible class of exponential family distributions on manifolds such as the torus, sphere, and rotation groups, and show that for these distributions the gradient of the log-likelihood can be computed efficiently using a non-commutative generalization of the Fast Fourier Transform (FFT). We discuss applications to Bayesian camera motion estimation (where harmonic exponential families serve as conjugate priors), and modelling of the spatial distribution of earthquakes on the surface of the earth. Our experimental results show that harmonic densities yield a significantly higher likelihood than the best competing method, while being orders of magnitude faster to train.Comment: fixed typ

A 17 degree of freedom anthropomorphic manipulator

A 17 axis anthropomorphic manipulator, providing coordinated control of two seven degree of freedom arms mounted on a three degree of freedom torso-waist assembly, is presented. This massively redundant telerobot, designated the Robotics Research K/B-2017 Dexterous Manipulator, employs a modular mechanism design with joint-mounted actuators based on brushless motors and harmonic drive gear reducers. Direct joint torque control at the servo level causes these high-output joint drives to behave like direct-drive actuators, facilitating the implementation of an effective impedance control scheme. The redundant, but conservative motion control system models the manipulator as a spring-loaded linkage with viscous damping and rotary inertia at each joint. This approach allows for real time, sensor-driven control of manipulator pose using a hierarchy of competing rules, or objective functions, to avoid unplanned collisions with objects in the workplace, to produce energy-efficient, graceful motion, to increase leverage, to control effective impedance at the tool or to favor overloaded joints

On Advanced Mobility Concepts for Intelligent Planetary Surface Exploration

Surface exploration by wheeled rovers on Earth's Moon (the two Lunokhods) and Mars (Nasa's Sojourner and the two MERs) have been followed since many years already very suc-cessfully, specifically concerning operations over long time. However, despite of this success, the explored surface area was very small, having in mind a total driving distance of about 8 km (Spirit) and 21 km (Opportunity) over 6 years of operation. Moreover, ESA will send its ExoMars rover in 2018 to Mars, and NASA its MSL rover probably this year. However, all these rovers are lacking sufficient on-board intelligence in order to overcome longer dis-tances, driving much faster and deciding autonomously on path planning for the best trajec-tory to follow. In order to increase the scientific output of a rover mission it seems very nec-essary to explore much larger surface areas reliably in much less time. This is the main driver for a robotics institute to combine mechatronics functionalities to develop an intelligent mo-bile wheeled rover with four or six wheels, and having specific kinematics and locomotion suspension depending on the operational terrain of the rover to operate. DLR's Robotics and Mechatronics Center has a long tradition in developing advanced components in the field of light-weight motion actuation, intelligent and soft manipulation and skilled hands and tools, perception and cognition, and in increasing the autonomy of any kind of mechatronic systems. The whole design is supported and is based upon detailed modeling, optimization, and simula-tion tasks. We have developed efficient software tools to simulate the rover driveability per-formance on various terrain characteristics such as soft sandy and hard rocky terrains as well as on inclined planes, where wheel and grouser geometry plays a dominant role. Moreover, rover optimization is performed to support the best engineering intuitions, that will optimize structural and geometric parameters, compare various kinematics suspension concepts, and make use of realistic cost functions like mass and consumed energy minimization, static sta-bility, and more. For self-localization and safe navigation through unknown terrain we make use of fast 3D stereo algorithms that were successfully used e.g. in unmanned air vehicle ap-plications and on terrestrial mobile systems. The advanced rover design approach is applica-ble for lunar as well as Martian surface exploration purposes. A first mobility concept ap-proach for a lunar vehicle will be presented