By Takeo Igarashi, Mike Stilman (auth.), David Hsu, Volkan Isler, Jean-Claude Latombe, Ming C. Lin (eds.)
Robotics is on the cusp of dramatic transformation. more and more advanced robots with remarkable autonomy are discovering new purposes, from clinical surgical procedure, to development, to domestic providers. by contrast heritage, the algorithmic foundations of robotics have gotten extra an important than ever, with the intention to construct robots which are quickly, secure, trustworthy, and adaptive. Algorithms permit robots to understand, plan, keep watch over, and research. The layout and research of robotic algorithms elevate new primary questions that span machine technological know-how, electric engineering, mechanical engineering, and arithmetic. those algorithms also are discovering purposes past robotics, for instance, in modeling molecular movement and developing electronic characters for games and architectural simulation. The Workshop on Algorithmic Foundations of Robotics (WAFR) is a hugely selective assembly of major researchers within the box of robotic algorithms. in view that its production in 1994, it has released a few of the field’s most vital and lasting contributions. This e-book comprises the complaints of the ninth WAFR, hung on December 13-15, 2010 on the nationwide college of Singapore. The 24 papers integrated during this booklet span a wide selection of themes from new theoretical insights to novel applications.
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Extra info for Algorithmic Foundations of Robotics IX: Selected Contributions of the Ninth International Workshop on the Algorithmic Foundations of Robotics
Our key insight is that local path equivalence is an expressive and powerful tool that reveals shared outcomes in collision-testing. Specifically, two equivalent neighboring paths cover some common ground in the workspace, and between them lies a continuum of covered paths. We develop the mathematical foundations to detect equivalence relations among all local paths based on a finite precomputed path set. We then utilize these tools to devise efficient algorithms for detecting equivalence and implicitly collision-testing local paths.
N. Singh, and H. Durrant-Whyte Fig. 3 Three trajectories for a car (rectangle), all resulting from the same control input. The behaviour is sensitive to initial conditions (speed and turning rate), causing different trajectories. In general, equality of the third part of the control inputs, u3 , can not be used, as the final states of the middle segments, Φu (x0 , Iu+2 ) and Φu (x0 , Iv+2 ), need not coincide. Using different states as initial states for the third part of the path can result in a variety of different trajectories as illustrated in Fig.
At bottom: this plot, generated numerically, approximates the set of appropriate choices for v and w. The gray region at top right must be avoided, as we show in Lemma 2. Such choices would permit an obstacle to occur between two safe paths that obey (3). A path whose values fall in the white region is called an appropriate path. 1 Properties of Paths In this section, we establish a small set of conditions under which we can quickly determine that two paths are equivalent. We constrain path shape through two dimensionless ratios relating three physical parameters.