From spider robots to half disk robots

International audienceWe study the problem of computing the set F of accessible and stable placements of a spider robot. The body of this robot is a single point and the legs are line segments attached to the body. The robot can only put its feet on some regions, called the foothold regions. Moreover, the robot is subject to two constraints: Each leg has a maximal extension R (accessibility constraint) and the body of the robot must lie above the convex hull of its feet (stability constraint). We present an efficient algorithm to compute F. If the foothold regions are polygons with n edges in total, our algorithm computes F in O(n^2 log n) time and O(n^2 alpha(n)) space where alpha is the inverse of the Ackerman's function. Omega(n^2) is a lower bound for the size of F

Motion Planning of Legged Robots

We study the problem of computing the free space F of a simple legged robot called the spider robot. The body of this robot is a single point and the legs are attached to the body. The robot is subject to two constraints: each leg has a maximal extension R (accessibility constraint) and the body of the robot must lie above the convex hull of its feet (stability constraint). Moreover, the robot can only put its feet on some regions, called the foothold regions. The free space F is the set of positions of the body of the robot such that there exists a set of accessible footholds for which the robot is stable. We present an efficient algorithm that computes F in O(n2 log n) time using O(n2 alpha(n)) space for n discrete point footholds where alpha(n) is an extremely slowly growing function (alpha(n) <= 3 for any practical value of n). We also present an algorithm for computing F when the foothold regions are pairwise disjoint polygons with n edges in total. This algorithm computes F in O(n2 alpha8(n) log n) time using O(n2 alpha8(n)) space (alpha8(n) is also an extremely slowly growing function). These results are close to optimal since Omega(n2) is a lower bound for the size of F.Comment: 29 pages, 22 figures, prelininar results presented at WAFR94 and IEEE Robotics & Automation 9

Comparison of Spider-Robot Information Models

The paper deduces a mathematical model of a spider-robot with six three-link limbs. Many limbs with a multi-link structure greatly complicate the process of synthesizing a model, since in total the robot has twenty-four degrees of freedom, i.e., three coordinates of the center of mass of the body in space, three angles of rotation of the body relative to its center of mass and three degrees of freedom for each limb, to describe the position of the links. The derived mathematical model is based on the Lagrange equations with a further transformation of the equations to the Cauchy normal form in a matrix form. To test the resulting model in a SimInTech environment, an information model is synthesized and two simple experiments ar carried out to simulate the behavior of real spiders: moving forward in a straight line and turning in place at a given angle. The experimental results demonstrate that the synthesized information model can well cope with the tasks and the mathematical model underlying it can be used for further research

Motion Planning and Reconfiguration for Systems of Multiple Objects

This chapter surveys some recent results on motion planning and reconfiguration for systems of multiple objects and for modular systems with applications in robotics.

Australasian Arachnology, Number 72, August 2005

Just days before this newsletter went to the printer, the Australasian Arachnological Society launched its own website: www.australasian-arachnology.org It was a great effort from all involved, but two people in particular (who are not even directly involved with our society) deserve a special mention: Randolf Manderbach (web programming) and Thomas García Godines (graphic design) professionally developed and programmed the lay-out of our website, for free! Thanks to both of them! You will find further acknowledgements and some information in regard to the ‘philosophy’ of our site in an introductory article on page 4. Similar to this newsletter, the website will prosper only through contributions and feedback from all of you