Ein Algorithmus für das allgemeine geometrische Bewegungsplanungsproblem wird vorgestellt, welcher intuitiv leichte Probleme auch in Szenen mit vielen Freiheitsgraden schnell löst. Eine Divide-and-Conquer-Strategie dient zur Wegesuche, wobei der Konfigurationsraum nie explizit errechnet oder repräsentiert wird; sie greift auf eine Routine zur Kollisionserkennung zurück. Die elementaren Translationen und Rotationen, aus denen sich eine Bewegung zusammensetzt, werden getrennt durch ein effizientes Verfahren behandelt; Hüllkörper verringern dabei die Laufzeit in praktischen Beispielen dramatisch.

We present a general heuristic approach to the geometric motion planning problem with the aim to quickly solve intuitively simple problems. It is based on a divide-and-conquer path search strategy which makes inquiries about feasible paths; to answer these, we develop an efficient collision detection scheme that handles translations and rotations of polyhedra to compute all times of collision. The whole algorithm can be easily implemented and universally applied and has been successfully tested in a program for assembly planning.

We present a general heuristic approach to the geometric motion planning problem with the aim to quickly solve intuitively simple problems. It is based on a divide-and-conquer path search strategy which makes inquiries about feasible paths; to answer these, we develop an efficient collision detection scheme that handles translations and rotations of polyhedra to compute all times of collision. The whole algorithm can be easily implemented and universally applied and has been successfully tested in a program for assembly planning.

We present a heuristic approach to geometric path planning with movable obstacles. Treating movable obstacles as mobile robots leads to path planning problems with many degrees of freedom which are intractable. Our strategy avoids this computational complexity by decoupling the whole motion planning problem into a series of tractable problems, which are solved using known path planning algorithms. The individually computed solutions are then coordinated to a path plan. This method results in a powerful and practicable strategy for path planning with movable obstacles, which can be applied using a wide variety of known motion planning algorithms.

In this paper we present some results about analytic machines regarding the power of computations over Q or R, solutions of differential equations and the stability problem of dynamical systems. We first explain the machine model, which is a kind of sf Blum-Shub-Smale machine enhanced by infinite convergent computations. Next, we compare the computational power of such machines over the fields Q and R showing that finite computations with real numbers can be simulated by infinite converging computations on rational numbers, but the precision of the approximation is not known during the process. Our attention is then shifted to ordinary differential equations (ODEs), dynamical systems described by ODEs and the undecidability of a class of stability problems for dynamical systems.