The complexity of exact motion planning algorithms highly depends on the complexity of the robot’s free space, i.e., the set of all collision-free placements of the robot. Theoretically, the complexity of the free space can be very high. In practice, the complexity of the free space tends to be much smaller. We show that, under some realistic assumptions, the complexity of the free space of a r...

Motion planning is a fundamental problem in robotics. It comes in a variety of forms, but the simplest version is as follows. We are given a robot system B, which may consist of several rigid objects attached to each other through various joints, hinges, and links, or moving independently, and a 2D or 3D environment V cluttered with obstacles. We assume that the shape and location of the obstac...

Motion planning is a fundamental problem in robotics. It comes in a variety of forms, but the simplest version is as follows. We are given a robot system B, which may consist of several rigid objects attached to each other through various joints, hinges, and links, or moving independently, and a 2D or 3D environment V cluttered with obstacles. We assume that the shape and location of the obstac...

This paper presents a novel on-line trajectory planning method for the autonomous robotic interception of moving targets in the presence of dynamic obstacles, i.e., position and velocity matching (also referred to as rendezvous). The novelty of the proposed time-optimal interception method is that it directly considers the dynamics of the obstacles as well as the target in its interception mane...

Brains and sensory systems evolved to guide motion. Central to this task is controlling the approach to stationary obstacles and detecting moving organisms. Looming has been proposed as the main monocular visual cue for detecting the approach of other animals and avoiding collisions with stationary obstacles. Elegant neural mechanisms for looming detection have been found in the brain of insect...