Path-Parameterised RRTs for Underactuated Systems

TL;DR

A specialised state-based steering mechanism within an RRT motion planning algorithm is developed, enabling the generation of both geometric paths and their time parameterisations without introducing excessive computational overhead.

Abstract

We present a sample-based motion planning algorithm specialised to a class of underactuated systems using path parameterisation. The structure this class presents under a path parameterisation enables the trivial computation of dynamic feasibility along a path. Using this, a specialised state-based steering mechanism within an RRT motion planning algorithm is developed, enabling the generation of both geometric paths and their time parameterisations without introducing excessive computational overhead. We find with two systems that our algorithm computes feasible trajectories with higher rates of success and lower mean computation times compared to existing approaches.

Figures (5)

• Figure 1: Visualisation of tree-growth in UA1-RRT, with edges $V_i.\bm{\mathcal{P}}$ connecting vertices $V_i$ in obstacle-free configuration space $\mathcal{Q}$. Path are added as edges to the tree if their path rate squared $\theta$ (magenta) remains positive (red) and discarded if a zero-crossing is encountered (blue).
• Figure 2: Underactuated degree-one (UA1) example systems.
• Figure 3: Percentage of successful attempts vs. computation time for the UAV and acrobot examples.
• Figure 4: UAV trajectories found by each method (feasible components of resulting trajectories shown).
• Figure 5: Example acrobot motions for UA1-RRT (left) and KNN-RRT (right) with profiles $\bm{q}(t)$ and $\bm{\tau}(t)$.

Theorems & Definitions (1)

• Definition II.1: Dynamic Feasibility