1. Spring Berman MEAM 620 Project March 20, 2006 Simulation of Robot Guidance through Star Worlds via Navigation Functions

2. Problem Statement qiqi qdqd Assume: Construct a smooth, bounded-torque controller  such that the robot trajectory goes to q d while avoiding the obstacles. Point robot Stationary 2D world Ideal sensors, perfect information Ideal actuators Traditionally: Path planning + trajectory planning + robot control Navigation function approach

3. Properties of a navigation function Smooth (at least C 2 ) Morse: nonsingular Hessian at critical points Admissible: uniformly maximal on boundary of Polar: unique minimum at q d Properties are invariant under C q diffeomorphisms (q  1) Nav fn on F Nav fn on M

4. Sphere and Star Worlds Sphere world nav fn Star world nav fn where on obstacles : Analytic switches : Star-to-sphere transformation qdqd

5. Constructed Navigation Functions Sphere World Next: Generate controller; simulate robot navigation Investigate complexity as a function of # obstacles  = 4.6 Star World  = 10, λ = 75

6. References