Approximate Time-Optimal Trajectories for Damped Double Integrator in 2D Obstacle Environments under Bounded Inputs
This work addresses trajectory planning for robotic or autonomous systems in cluttered environments, but it is incremental as it builds on prior methods.
The authors tackled the problem of planning time-optimal trajectories for agents with damped double integrator dynamics in 2D obstacle environments under bounded inputs, by extending existing path-velocity decomposition methods to include a C^1-Tangent graph for smooth paths and providing analytical expressions for near time-optimal velocity profiles.
This article provides extensions to existing path-velocity decomposition based time optimal trajectory planning algorithm \cite{kant1986toward} to scenarios in which agents move in 2D obstacle environment under double integrator dynamics with drag term (damped double integrator). Particularly, we extend the idea of a tangent graph \cite{liu1992path} to $\calC^1$-Tangent graph to find continuously differentiable ($\calC^1$) shortest path between any two points. $\calC^1$-Tangent graph has a continuously differentiable ($\calC^1$) path between any two nodes. We also provide analytical expressions for a near time-optimal velocity profile for an agent moving on these shortest paths under the damped double integrator with bounded acceleration.