In this paper, we present improved spline fitting techniques with the application of trajectory teaching for mobile robots. Given a recorded reference trajectory, we apply non-linear least-squares optimization to accurately approximate the trajectory using a parametric spline. The fitting process is carried out without fixed correspondences between data points and points along the spline, which improves the fit especially in sharp curves. By using a specific path model, our approach requires substantially fewer free parameters than standard approaches to achieve similar residual errors. Thus, the generated paths are ideal for subsequent optimization to reduce the time of travel or for the combination with autonomous planning to evade obstacles blocking the path. Our experiments on real-world data demonstrate the advantages of our method in comparison with standard approaches.

This paper presents a novel approach to kino-dynamic trajectory generation for non-circular omnidirectional platforms that can be combined with existing path planners. We use quintic Bézier splines to specify position and orientation of the holonomic robot for every point in time. To fully exploit the capabilities of the holonomic robot we propose a novel path representation. It allows for continuous variation of path shapes in the spectrum between straight-line paths with turns on the spot and smooth paths with independent rotations and translations. Using this representation our method optimizes trajectories according to a user-defined cost function, considering the constraints of the platform. This way, it generates fast and efficient trajectories in an anytime fashion. The experiments carried out on an industrial robot show that our approach generates highly efficient and smooth motion trajectories that can be tracked with high precision and predictability. Furthermore, the system operates in real-world environments containing unmapped obstacles and narrow passages.

This paper presents novel, highly efficient approaches for updating Euclidean distance maps and Voronoi diagrams represented on grid maps. Our methods employ a dynamic variant of the brushfire algorithm to update only those cells that are actually affected by changes in the environment. In experiments in different environments we show that our update strategies for distance maps and Voronoi diagrams require substantially fewer cell visits and significantly less computation time compared to previous approaches. Furthermore, the dynamic Voronoi diagram also improves on previous work by correctly dealing with non-convex obstacles such as building walls. We also present a dynamic variant of a skeletonization-based approach to Voronoi diagrams that is especially robust to noise. All of our algorithms consider actual Euclidean distances rather than grid steps. An open source implementation is available online.

People in densely populated environments typically form groups that split and merge. In this paper we track groups of people so as to reflect this formation process and gain efficiency in situations where maintaining the state of individual people would be intractable. We pose the group tracking problem as a recursive multi-hypothesis model selection problem in which we hypothesize over both, the partitioning of tracks into groups (models) and the association of observations to tracks (assignments). Model hypotheses that include split, merge, and continuation events are first generated in a data-driven manner and then validated by means of the assignment probabilities conditioned on the respective model. Observations are found by clustering points from a laser range finder given a background model and associated to existing group tracks using the minimum average Hausdorff distance. Experiments with a stationary and a moving platform show that, in populated environments, tracking groups is clearly more efficient than tracking people separately. Our system runs in real-time on a typical desktop computer.

This paper presents an approach to time-optimal kinodynamic motion planning for a mobile robot. A global path planner is used to generate collision-free straight-line paths from the robot's position to a given goal location. With waypoints of this path, an initial trajectory is generated which defines the planned position of the robot over time. A velocity profile is computed that accounts for constraints on the velocity and acceleration of the robot. The trajectory is refined to minimize the time needed for traversal by an any-time optimization algorithm. An error-feedback controller generates motor commands to execute the planned trajectory. Quintic Be¿zier splines are used to allow for curvature-continuous joins of trajectory segments, which enables the system to replan trajectories in order to react to unmapped obstacles. Experiments on real robots are presented that show our system's capabilities of smooth, precise, and predictive motion.