FRTree Planner: Robot Navigation in Cluttered and Unknown Environments with Tree of Free Regions

TL;DR

FRTree planner introduces a map-free navigation framework that constructs a dynamic tree of free regions to capture the geometry and topology of collision-free space in cluttered, unknown environments. The method continuously expands along interesting directions inferred from local perception, prunes infeasible branches using the robot’s geometry, and selects intermediate goals via a greedy, backtracking-aware strategy. A geometry-aware bi-level trajectory optimization, incorporating SOS-based region scaling into an ALTRO-based solver, ensures safe, collision-free motion through narrow passages. Through simulations and real-world tests on a Unitree GO1, FRTree demonstrates real-time performance and improved safety and efficiency over baselines in highly cluttered terrains without prior maps.

Abstract

In this work, we present FRTree planner, a novel robot navigation framework that leverages a tree structure of free regions, specifically designed for navigation in cluttered and unknown environments with narrow passages. The framework continuously incorporates real-time perceptive information to identify distinct navigation options and dynamically expands the tree toward explorable and traversable directions. This dynamically constructed tree incrementally encodes the geometric and topological information of the collision-free space, enabling efficient selection of the intermediate goals, navigating around dead-end situations, and avoidance of dynamic obstacles without a prior map. Crucially, our method performs a comprehensive analysis of the geometric relationship between free regions and the robot during online replanning. In particular, the planner assesses the accessibility of candidate passages based on the robot's geometries, facilitating the effective selection of the most viable intermediate goals through accessible narrow passages while minimizing unnecessary detours. By combining the free region information with a bi-level trajectory optimization tailored for robots with specific geometries, our approach generates robust and adaptable obstacle avoidance strategies in confined spaces. Through extensive simulations and real-world experiments, FRTree demonstrates its superiority over benchmark methods in generating safe, efficient motion plans through highly cluttered and unknown terrains with narrow gaps.

Figures (6)

• Figure 1: Overview of the proposed navigation framework. (a) Illustration of the framework pipeline. At each replanning phase, a tree of free regions is dynamically constructed to efficiently embed information about the free space and potential exploration directions. The next feasible and explorable intermediate goal is inferred and fed into the subsequent geometry-aware bi-level trajectory optimization framework to achieve safe and efficient navigation in unknown and cluttered environments with narrow passages and bug traps. (b) Visualization of the navigation process with limited sensor range. As navigation progresses, the free region tree is continuously updated that records visited and dead-end areas. This enables the consistent selection of suitable intermediate goals, ensuring safe and efficient navigation to the destination.
• Figure 2: Illustration of the dynamic tree construction. (a) Visualization of the process for identifying the interesting directions. (b) Depiction of the free regions sequence generation for each node along its interesting direction $r$. (c) Process of pruning infeasible paths at narrow passages. We evaluate the qualities of the free regions $\mathcal{Q}_A$, $\mathcal{Q}_B$, and their intersection $\mathcal{Q}_{A,B}$ to ensure the safe transition from $\mathcal{Q}_A$ to $\mathcal{Q}_B$. We search among $a-e$ (vertices of the intersection $\mathcal{Q}_{A,B}$) to find the shortest line segment $be$ (shown in red) that intersects the reference path from $\mathcal{Q}_A$ to $\mathcal{Q}_B$ (the line segments connecting $\boldsymbol{C}(\mathcal{Q}_{A})$, $\boldsymbol{C}(\mathcal{Q}_{A,B})$, and $\boldsymbol{C}(\mathcal{Q}_{B})$).
• Figure 3: An example of intermediate goal selection during navigation. At the current node (shown in yellow), we first add all the child nodes and the second-best child node of its parent (if it exists) to a candidate intermediate goal set $\boldsymbol{\mathcal{M}}$ (the red dashed lines). We then select the node with the minimum estimated cost from $\boldsymbol{\mathcal{M}}$ as the current intermediate goal (the black node). Black dashed lines represent unexplored nodes in $\mathcal{T}$, while black solid lines represent visited paths. Notably, in unknown environments, if a dead end is encountered as in (d), the process backtracks (the red solid lines) till it finds the parent node with other feasible nodes for further exploration using the connectivity information of $\mathcal{T}$.
• Figure 4: Performance of our proposed navigation framework in the maze scenario.
• Figure 5: Visualization of three selected trajectories generated from our methods in the forest environment ($15\,\textup{m}\times5\,\textup{m}$). Our method efficiently and safely navigates through narrow terrains of varying obstacle densities exploiting the dynamically constructed free region tree considering specific robot geometries with no prior map.