Hybrid and Oriented Harmonic Potentials for Safe Task Execution in Unknown Environment

TL;DR

This work proposes an efficient and automated scheme to construct harmonic potentials incrementally online as guided by the task automaton and introduces a novel two-layer harmonic tree (HT) structure that facilitates the hybrid combination of oriented search algorithms for task planning and harmonic-based navigation controllers for non-holonomic robots.

Abstract

Harmonic potentials provide globally convergent potential fields that are provably free of local minima. Due to its analytical format, it is particularly suitable for generating safe and reliable robot navigation policies. However, for complex environments that consist of a large number of overlapping non-sphere obstacles, the computation of associated transformation functions can be tedious. This becomes more apparent when: (i) the workspace is initially unknown and the underlying potential fields are updated constantly as the robot explores it; (ii) the high-level mission consists of sequential navigation tasks among numerous regions, requiring the robot to switch between different potentials. Thus, this work proposes an efficient and automated scheme to construct harmonic potentials incrementally online as guided by the task automaton. A novel two-layer harmonic tree (HT) structure is introduced that facilitates the hybrid combination of oriented search algorithms for task planning and harmonic-based navigation controllers for non-holonomic robots. Both layers are adapted efficiently and jointly during online execution to reflect the actual feasibility and cost of navigation within the updated workspace. Global safety and convergence are ensured both for the high-level task plan and the low-level robot trajectory. Known issues such as oscillation or long-detours for purely potential-based methods and sharp-turns or high computation complexity for purely search-based methods are prevented. Extensive numerical simulation and hardware experiments are conducted against several strong baselines.

Figures (15)

• Figure 1: Left: Illustration of the proposed framework, which consists of the initial synthesis, the online adaption of the task plan and harmonic potentials, and the squircle estimation. Right: Oscillations and long detours might occur via classic navigation functions as shown in the red, violet and blue trajectories.
• Figure 2: Illustration of the diffeomorphic transformation from sphere word $\mathcal{M}$ to bounded point world $\Tilde{\mathcal{P}}$ and to unbounded point world $\mathcal{P}$.
• Figure 3: Left: Robot in the workspace with overlapping squircles and several regions of interest. Right: Estimated (in black) and inflated (in blue) obstacles.
• Figure 4: (a) Squircles with the parameter $\varkappa=0.6$ and $\varkappa=0.99$; (b) Ray scaling process. The boundary of the star-shaped obstacle is mapped onto the boundary of a sphere (Left). The boundary of the child obstacle is mapped onto a segment of the boundary of the parent obstacle (Right).
• Figure 5: Estimated squircles (in blue dashed lines) under different curvatures $\kappa$ and different distributions of (a) accurate or (b) noisy measurements.

Theorems & Definitions (33)

• Definition 1
• Definition 2
• Lemma 1
• proof
• Remark 1
• Lemma 2
• proof
• Definition 3
• Lemma 3
• proof