---
kind: concept
slug: frontier-exploration
title: Frontier exploration
summary: >-
  Chooses the next goal at frontiers, the cells where explored free space meets unexplored space, then drives there. Two variants: learned frontier potentials that find a named object without RL (PONI, author-reported Gibson val SPL 41.0), and information-based utilities on frontiers in active SLAM (a survey with no experiments). Choose by goal type, segmentation quality and localisation risk.
tags: [robotics, exploration, navigation, active-slam]
papers: ["2201.10029", "2207.00254"]
related: [semantic-occupancy-mapping, simultaneous-localization-and-mapping, partially-observable-markov-decision-process, mutual-information-maximization, multi-robot-navigation]
status: draft
updated_at: 2026-11-03
---

## Overview

A robot that maps unknown space has to pick where to go next. A frontier is an
explored free cell that touches unexplored space. Any route into unseen space
crosses a frontier, so the choice of goal can be limited to frontiers
[arxiv:2201.10029 §3.3]. The modular active SLAM pipeline follows the same
pattern: list candidate goals, score each one with a utility, and go to the
best [arxiv:2207.00254 §2.2].

The invariant all variants share is the selection rule: the goal is the
candidate with the highest score, and a planner then drives the robot there
[arxiv:2201.10029 §3.3] [arxiv:2207.00254 eq. 24]. The variants differ in where
the score comes from. One learns it from maps that already exist. The other
computes it from the robot's own uncertainty.

## Variants

### Learned frontier potentials for object goals

A small image-to-image network reads a partial top-down semantic map. For each
frontier it predicts two values: how much unexplored room lies beyond it, and
how close it is to a named object category [arxiv:2201.10029 §3.3]. The two
values are averaged with equal weight, and the frontier with the highest value
becomes the goal. A Fast Marching planner then moves the agent there, with no
learned policy in the loop [arxiv:2201.10029 §3.2, §3.5]. Card:
[PONI](/papers/2201.10029).

The network is trained with a supervised mean-squared-error loss. Its
training examples are partial maps cut from complete semantic maps of
scenes, and the targets come from the complete maps [arxiv:2201.10029 §3.6].
The paper reports 400,000 training tuples per dataset [arxiv:2201.10029 §4.2].
Author-reported results on the ObjectGoal task: Gibson validation success 73.6
and SPL 41.0; MP3D validation success 31.8 and SPL 12.1 [arxiv:2201.10029
tab. 1]. The paper reports training cost up to 1,600 times lower than the MP3D
method THDA, measured in GPU-hours [arxiv:2201.10029 §5].

### Information utilities on frontiers in active SLAM

Active SLAM is cast as a POMDP over the joint state of robot and map, and the
robot's action should reduce uncertainty [arxiv:2207.00254 §2.1]. Many of the
surveyed systems take frontiers as candidate goals. In the survey's condensed
table, 13 of 24 rows list frontiers among their goal candidates [arxiv:2207.00254
tab. 1]. Each candidate is scored by an expected information gain, such as
mutual information [arxiv:2207.00254 eq. 14], or by an optimal-design criterion
such as D-optimality, A-optimality or E-optimality [arxiv:2207.00254 eq. 19]
[arxiv:2207.00254 eq. 20] [arxiv:2207.00254 eq. 21]. The survey is a review and
runs no experiments of its own [arxiv:2207.00254 §1]. Card:
[A Survey on Active SLAM](/papers/2207.00254).

## When to use which

| Situation | Use | Why |
|---|---|---|
| Goal is a named object category, semantic maps are available, and training compute is limited | Learned frontier potentials | No RL is needed, and training runs on passive maps [arxiv:2201.10029 §3.6, §5]. Reported Gibson and MP3D results are in [arxiv:2201.10029 tab. 1]. |
| Goal is generic coverage, or no object term is wanted | Area potential alone | On Gibson validation, an area-only setting reaches success 72.7 against 73.6 with both terms [arxiv:2201.10029 tab. 3]. |
| Semantic segmentation is unreliable or unavailable | Not the learned object term | Replacing predicted segmentation with ground truth raises success by 14.9 points on Gibson and 45.4 on MP3D [arxiv:2201.10029 supp. §S1, tab. S1]. |
| Localisation error is the main risk, and the robot must return to known places | Information utilities on frontiers, with a belief model | The survey treats the utility as a function of the belief and lists revisiting among candidate types [arxiv:2207.00254 §2.1] [arxiv:2207.00254 tab. 1]. |
| Robot can only use a learned policy trained end to end | Neither card | The survey mentions deep reinforcement learning but gives no numbers for it [arxiv:2207.00254 §7]. |

Pitfalls:

- PONI assumes noise-free depth and odometry in simulation [arxiv:2201.10029 §4].
  It does not model localisation uncertainty, so the active SLAM concern does
  not apply to it.
- The object cutoff distance is not given in the paper. It was chosen on
  validation data [arxiv:2201.10029 §3.3].
- Area normalisation differs by dataset. The paper divides by total free space
  of the complete map, but uses a fixed constant on MP3D [arxiv:2201.10029 §3.3].
- Table 1 of PONI has no variance, and its Gibson margin over SemExp is 1.9
  points of success [arxiv:2201.10029 tab. 1].
- On the MP3D test-standard challenge, PONI is best on SPL, SoftSPL and DTS but
  not on success [arxiv:2201.10029 tab. 2].
- The survey gives no algorithm to implement. Its joint-entropy sum is an
  approximation, and the weights it says are needed are not given [arxiv:2207.00254 §4.2].
- The survey states that the monotonic growth of uncertainty depends on the
  representation, not only on the criterion [arxiv:2207.00254 §4.3].

## Implementation sketch

Common core of both variants. Candidates are frontiers only. The score function
is the variant-specific part. The sketch is not a reference implementation.

```pseudocode
# One frontier-exploration step  [arxiv:2201.10029 §3.3]
# Input:  explored, free: (M, M) bool masks of the partial map
#         score_fn(cell) -> float, learned or information-based
# Output: goal cell for the local planner

def next_frontier_goal(explored, free, score_fn):
    # A frontier is an explored free cell next to unexplored space [§3.3]
    frontier = free_cells_adjacent_to_unexplored(explored, free)
    if not frontier:
        return None  # nothing left to explore
    # Score each candidate: PONI averages area and object potentials
    # [arxiv:2201.10029 eq. 2]; the survey uses an information utility
    # on the belief [arxiv:2207.00254 §4]
    scores = {cell: score_fn(cell) for cell in frontier}
    # Pick the best candidate; ties are not specified [arxiv:2201.10029 §3.3]
    return max(scores, key=scores.get)
```

## Contradictions

None known. The two sources score frontiers with different objectives: one
predicts a value for an object category, the other computes an information
measure on the belief [arxiv:2201.10029 §3.3] [arxiv:2207.00254 §4]. Their
numbers do not compare directly, because the survey reports no experiments.

## Papers

- [PONI: Potential Functions for ObjectGoal Navigation with Interaction-free Learning](/papers/2201.10029): learned area and object potentials at frontiers, with a Fast Marching planner.
- [A Survey on Active Simultaneous Localization and Mapping](/papers/2207.00254): formulation and modular pipeline for choosing frontier goals by information utility.