Motion Planning using Naturally Annoying Grammars (NAGs)

Motion planning is an important and fundamental problem in robotics. In all application of robotics, an indispensable part of the system is the ability to navigate through a complex environment without colliding with bothersome obstacles that can endanger the life of the autonomous agent. Specifically, given the environment with descriptions of the dynamics and obstacles, a starting position and a goal position, motion planning seeks to find a series of control inputs that can lead the robot from the starting position to the goal position, safely, without any collision with the obstacles. There has been a significant amount of work on this topic. In the 70s and 80s, the main approach for motion planning involved formulating a path in the configuration space (C-space) [2, 12]. Although these approaches implemented by constructing configuration space are complete (finding the path or reporting failure in limited amount of time), they are often computationally infeasible in high dimensional space with a large number of obstacles. More recently in the past 30 years, researchers rely more on sampling methods such as rapidly-exploring random trees (RRT) [11] or probabilistic roadmaps (PRM) [9]. Both of the methods are shown to be probabilistically complete. They relieve the burden of computing the C-space explicitly, and only require checking sample configurations of the robot for collisions. PRMs randomly sample points and compute a collision-free graph with the points, while RRTs construct a tree instead. Though some variants allow near optimal trajectories, all are limited to only solving feasible problems. All methods to date, leverage modern computational capabilities but forget to call upon a far more powerful tool, the grad student. This is mostly because grad students tend to be unreliable and fussy. We offer a novel approach to subdue this underutilized resource in the context of motion planning. We do so by efficiently enticing the grad student to be part of the algorithm. To our knowledge, no one has ever explored the usage of “natural grammar”, or