Shortest paths for finned, winged, legged, and wheeled vehicles with side-looking sensors

Sensor-guided robotic locomotion in different media often takes inspiration from natural examples, e.g. from fishes, birds, and humans for underwater, aerial, or walking robots, respectively. Interestingly, several naturalistic observations show that even very different species exhibit some similarities in their locomotion patterns: a notable one perhaps being the spiraling nature of paths that in some cases can be observed in sensory-guided tasks. As often conjectured in naturalistic studies, a common optimality principle may underpin such motion behaviors. We show in a robotics framework that spiraling motions appear in the solution of the problem of minimum path length. In particular, we study optimal paths for a simple model of finned, winged, and legged robotic vehicles, under different constraints on the field-of-view of the available sensory inputs. After showing that logarithmic spirals are indeed extremals of a sensory-constrained shortest path problem, we provide a complete synthesis of the optimal control for different robotic vehicles. Applications of these results to robotics can reduce the length of paths to be followed by underwater, aerial or legged robots to reach targets in their environment. The work also provides some interesting, although preliminary, insights into how sensory field-of-view limitations may influence motion patterns in natural systems.