Fuzzy Geometric Approach to Collision Estimation Under Gaussian Noise in Human-Robot Interaction

Humans and mobile robots while sharing the same work areas require a high level of safety especially at possible intersections of trajectories. An issue of the human-robot navigation is the computation of the intersection point in the presence of noisy measurements or fuzzy information. For Gaussian distributions of positions/orientations (inputs) of robot and human agent and their parameters the corresponding parameters at the intersections (outputs) are computed by analytical and fuzzy methods. This is done both for the static and the dynamic case using Kalman filters for robot/human positions and orientations and thus for the estimation of the intersection positions. For the overdetermined case (6 inputs, 2 outputs) a so-called ’energetic’ approach is used for the estimation of the point of intersection. The inverse task is discussed, specifying the parameters of the output distributions and looking for the parameters of the input distributions. For larger standard deviations (stds) mixed Gaussian models are suggested as approximation of non-Gaussian distributions.