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Path planning can be subject to different types of optimization. Some years ago a German researcher, U. Leuthäusser, proposed a new variational method for reducing most types of optimization criteria to one and the same: minimization of path length. This can be done by altering the Riemannian metric of the domain, so that optimal paths (with respect to whatever criterion) are simply seen as shortest. This method offers an extra feature, which has not been exploited so far: it admits direction–dependent criteria.

In this paper we make this feature explicit, and apply it to two different anisotropic settings. One is that of different costs for different directions: E.g. the situation of a countryside scene with ploughed fields. The second is dependence on oriented directions, which is called here "strong" anisotropy: the typical scene is that of a hill side. A covering projection solves the additional difficulty. We also provide some experimental results on synthetic data.

Unmanned aerial vehicles (UAVs) have recently attracted the attention of researchers due to their numerous potential civilian applications. However, current robot navigation technologies need further development for efficient application to various scenarios. One key issue is the “Sense and Avoid” capability, currently of immense interest to researchers. Such a capability is required for safe operation of UAVs in civilian domain. For autonomous decision making and control of UAVs, several path-planning and navigation algorithms have been proposed. This is a challenging task to be carried out in a 3D environment, especially while accounting for sensor noise, uncertainties in operating conditions, and real-time applicability. Heuristic and non-heuristic or exact techniques are the two solution methodologies that categorize path-planning algorithms. The aim of this paper is to carry out a comprehensive and comparative study of existing UAV path-planning algorithms for both methods. Three different obstacle scenarios test the performance of each algorithm. We have compared the computational time and solution optimality, and tested each algorithm with variations in the availability of global and local obstacle information.

In robotic demining, the robot relies on a path-planner capable of generating trajectories to search for all the mines while avoiding obstacles whose locations are unknown. Several families of coverage algorithms exist but there is only one that guarantees complete coverage, the exact cellular decomposition family. This paper details the modifications performed to a cellular decomposition method for unstructured environments for its application to walking robots. Experiments show preliminary results and improvements to the method are proposed.

Path-planning in dynamic environments while meeting safety requirements for robots and humans is an open problem in robotics. The successful navigation in this kind of environments requires a certain level of anticipation to the future behavior of moving objects. In this paper we propose the use of movement prediction in the generation of dynamic artificial potential fields (DAPF), which will allow the robot to navigate in highly dynamic environments with a major degree of safety and effectiveness, especially in cases where the obstacles and objectives move at higher velocities than the controlled robots. Our approach is based on previous works on potential and velocity fields with additional considerations to avoid the well known local minimum problem and to anticipate the predicted path of objects, our solution tries to maintain the reactive characteristics of the artificial potential fields. The proposed method was tested in a holonomic simulation with 100% better results for the same scenarios than the original fields without prediction.