Kinodynamic Motion Planning 1 Kinodynamic Motion Planning 5

Kinodynamic planning attempts to solve a robot motion problem subject to simultaneous kinematic and dynamics constraints. In the general problem, given a robot system, we must nd a minimal-time trajectory that goes from a start position and velocity to a goal position and velocity while avoiding obstacles by a safety margin and respecting constraints on velocity and acceleration. We consider the simpliied case of a point mass under Newtonian mechanics, together with velocity and acceleration bounds. The point must be own from a start to a goal, amidst polyhedral obstacles in 2D or 3D. While exact solutions to this problem are not known, we provide the rst provably good approximation algorithm, and show that it runs in polynomial time. Abstract: Kinodynamic planning attempts to solve a robot motion problem subject to simultaneous kinematic and dynamics constraints. In the general problem, given a robot system, we must nd a minimal-time trajectory that goes from a start position and velocity to a goal position and velocity while avoiding obstacles by a safety margin and respecting constraints on velocity and acceleration. We consider the simpliied case of a point mass under Newtonian mechanics, together with velocity and acceleration bounds. The point must be own from a start to a goal, amidst polyhedral obstacles in 2D or 3D. While exact solutions to this problem are not known, we provide the rst provably good approximation algorithm, and show that it runs in polynomial time.