A Survey on Active Simultaneous Localization and Mapping: State of the Art and New Frontiers

In plain words

A robot that builds a map of a room while finding out where it is in that room has to decide where to drive next. Driving to new places reveals more of the map, but the robot's position estimate gets less certain the longer it goes without seeing something it already knows. Driving back to known places can fix that. Choosing the next move well is called active SLAM.

This survey looks at how researchers have framed and solved that choice. It gives one common mathematical description of the problem and shows the usual way of splitting it into three steps: pick candidate destinations, score each one, then go to the best. It then covers other routes, such as planning over whole paths, learning a policy with deep reinforcement learning, and coordinating several robots. It ends with open questions, such as how to know when to stop exploring and how to compare methods fairly.

TL;DR

A survey, not a method. Use it to find the standard formulation of active SLAM §2.1, the modular three-stage pipeline §2.2, the utility criteria used to score candidate moves §4 tab. 1 and the open questions §9. It gives no experiments and no reference implementation. Its numbers are claims of the cited works.

Problem

A robot must build a map of an unknown environment and localise itself in it, while also choosing its own motion. The paper treats this as active perception: the robot should act to improve its localisation and its map §1. The hard part is that the effect of a future action on uncertainty must be predicted before the action is taken §2.1. Exact solution of the resulting decision problem is intractable in general, so most methods simplify it §2.1 §2.2.

Method

This paper has no method to implement. Its parts are a formulation, a pipeline, a set of utility functions and surveys of alternatives. The implementable content is the set of equations below. Numbers are the paper's equation numbers as they appear in the compiled text §2 §4 §5.

1. Formulation §2.1. Active SLAM is cast as a POMDP with a belief over the joint state of robot and map. The belief is the posterior over states given the history of observations and actions eq. 1. The predicted belief after an action and a future observation is eq. 3, and the likelihood of an observation given a belief and an action is eq. 4.
2. Belief reward. The reward is written as an expectation over the belief, so that it depends on uncertainty rather than on a specific state eq. 5. The paper calls such utility functions a belief-dependent reward §2.1.
3. Simplified problem §2.1. If the future measurement is taken to be the most likely one eq. 8, and the horizon is finite, the discount and the expectation can be dropped. Planning then becomes a maximisation of the summed utility over a sequence of k actions eq. 9.
4. Modular pipeline §2.2 §3 §4 §5. Each cycle has three stages: (a) identify potential actions, usually goal locations; (b) compute a utility for each candidate; (c) select the best candidate and execute it.
5. Information-theoretic utility §4.2. The posterior entropy after an action is approximated as the sum of a robot-entropy term and a map-entropy term, with the cross term given in eq. 10 and eq. 11. Robot entropy is a Gaussian log-determinant eq. 12. Map entropy for discrete occupancy cells is a sum over cells of occupancy-based terms eq. 13. Mutual information, the expected reduction of entropy, is eq. 14. KL divergence between prior and posterior is eq. 15.
6. Optimal-design utility §4.3. For a Gaussian posterior with covariance Σ, Kiefer's family of mappings is eq. 16, with its piecewise form in eq. 17. The named criteria are T-optimality eq. 18, D-optimality eq. 19, A-optimality eq. 20 and E-optimality as the smallest and largest eigenvalue eq. 21 eq. 22.
7. Action selection §5. For a discrete candidate set, the best action is the minimiser of the covariance criterion, equivalently the maximiser of the FIM-based criterion eq. 23. For information utilities it is the maximiser of mutual information, equivalently the minimiser of posterior entropy eq. 24.

# Modular active SLAM loop, as the survey describes it  [§2.2] [§3] [§4] [§5]
# Input:  current SLAM posterior; candidate set generator
# Output: next goal to execute

def active_slam_step(posterior):
    # Stage 1: reduce the search space to a set of candidate goals  [§3]
    candidates = identify_goals(posterior)
    # Stage 2: score each candidate by expected uncertainty after reaching it  [§4]
    for goal in candidates:
        utilities[goal] = expected_utility(posterior, goal)
    # Stage 3: pick the best candidate and execute a path to it  [§5] [eq. 24]
    return argmax(utilities)

Map and robot are often treated as independent Gaussians, and the survey notes that some representations keep them joint §2.1. The survey also lists three alternative families that do not split the problem into these stages: belief-space planning and continuous optimisation §6, deep reinforcement learning §7 and multi-robot formulations §8.

Hyperparameters

Not applicable: the paper trains and releases no model. The only quantitative settings it reports belong to cited studies and are not used here.

No table: the paper gives no hyperparameter values of its own. The horizon k in eq. 9 is a symbol with no value stated §2.1.

Results

No experiments. The paper reports two counts of its own, both from external sources, and no performance numbers.

Table I condenses the surveyed works by SLAM approach, map, goal candidates, utility and whether code is public, as the authors classify them tab. 1. The authors' classification is not checked by this card.

Table I, condensed from tab. 1

Table II compares the topics covered by this survey and by the two earlier surveys it names, Cadena et al. (2016) and Lluvia et al. (2021) tab. 2. The earlier surveys are described in §1.

Paper vs code

No official code. The LaTeX source contains no repository, project page or code link. A GitHub repository search for "active slam survey" returned no results. A broader search for "active slam" returned several repositories under other owners, none described as the survey's code. One repository, under the first author's account, is an active graph-SLAM code base. It is not linked from this paper and does not describe this survey, so it is not used.

Pitfalls

• No algorithm to implement. The survey gives formulations, not a method. Anyone implementing an active SLAM system must take each step from the cited works, and the survey does not say which cited work to use for which setting.
• Equation numbers follow the source. Numbers eq. 1 to eq. 24 count the numbered rows in the LaTeX source, skipping commented-out blocks. The arXiv version used is v2 (updated 2023-02-13). The source header states acceptance in IEEE Transactions on Robotics, so the journal layout may differ.
• Belief reward and POMDP reward differ. A POMDP reward depends on state and action. Belief-based utilities need a different form, which the paper handles through an extension of the POMDP §2.1 eq. 5. Implementers should take the belief reward, not a state reward, when scoring candidate moves.
• Simplifications are strong. The reduction to eq. 9 assumes the most likely future measurement eq. 8 and drops the expectation. The Gaussian robot-state assumption and the independence of map and robot are also stated as simplifications §2.1.
• Joint entropy is approximated. The sum in eq. 11 approximates the joint entropy of eq. 10. The two terms can differ greatly in magnitude, and the paper says weighting parameters are then needed §4.2. It names no value for these weights.
• Map entropy assumes independent cells. The occupancy-entropy formula eq. 13 holds only under that assumption §4.2.
• Monotonicity depends on representation. The paper reports that D-optimality alone guarantees monotonic growth of uncertainty in one analysis, and that other work says the representation of error decides monotonicity, not the criterion §4.3. The two claims conflict unless the representation is fixed.
• Numerical trap in determinants. The paper notes that the raw determinant criterion can produce precision errors when some variances are very small, and that Kiefer's family avoids this §4.3 eq. 16. The text names no tolerance.
• Eigenvalue criteria are limits. E-optimality eq. 21 eq. 22 is written as a min and max of eigenvalues. The paper describes it as a limit of the Kiefer family as p goes to plus or minus infinity §4.3. Implementers should use the eigenvalue form directly.
• Reported speed-ups are not given with setups. The claimed reductions in computation time for graph-based connectivity criteria are stated without numbers §4.4.
• Table I's code column is the authors' classification. It is not checked against the repositories, and the paper does not give the date of each check.
• Self-citation. Several works the survey discusses are by its own authors, including Placed, Carrillo, Indelman, Carlone and Castellanos. Their results are reported as the cited works state them §4.4 §9.5.
• Dated coverage. The survey covers work up to 2022. Its own statements about the state of deep learning and open problems are dated accordingly.
• Figures. The source contains figures only in commented-out blocks, so this paper has no compiled figures. Table I is a sideways table in the PDF.

Lineage

• Builds on: the earlier survey of Cadena et al. (2016) and the survey of Lluvia et al. (2021) §1 tab. 2. Both are named in the text, neither is in this wiki.
• Compared against: the two earlier surveys, on topic coverage tab. 2.
• Superseded by: not known from content already in this wiki.
• Publication venue, from the LaTeX source: IEEE Transactions on Robotics, stated as accepted.