Informed Baseline Search (IBS) Overview

• Informed Baseline Search (IBS) is an informed, anytime sampling-based framework that unifies A*-like graph search with incremental random sampling for continuous path planning.
• It employs admissible heuristics to order the exploration of an implicit random geometric graph, focusing on states and edges capable of improving the current solution.
• IBS achieves asymptotic optimality and practical anytime behavior by refining its search through batchwise sampling and efficient heuristic-guided queue management.

Searching arXiv for the BIT* paper to ground the article and citations. Informed Baseline Search (IBS), as reconstructed from the principles of Batch Informed Trees (BIT*), is an informed, anytime sampling-based search framework for continuous path planning that unifies graph-based heuristic search with incremental sampling over continuous domains. In this formulation, the planning problem is treated as search on an implicit random geometric graph (RGG), while admissible heuristics order both vertex expansion and edge evaluation by potential solution quality. The resulting framework combines A*-like search ordering with the asymptotic refinement of sampling-based planning, and is designed to focus computation on subsets of the state space that can still improve the current best solution (Gammell et al., 2017).

1. Conceptual provenance and defining characteristics

IBS is grounded in the same conceptual synthesis that defines BIT*: a direct unification of graph-based informed search, exemplified by A*, and sampling-based planning, exemplified by RRT* and PRM*. Graph-based informed search orders search on a fixed approximation by potential solution quality, typically via $g+h$, whereas sampling-based planning incrementally refines the approximation of a continuous domain through random samples. IBS inherits both ideas by building an implicit RGG over sampled states, maintaining an explicit spanning tree of that graph, and searching it in heuristic order (Gammell et al., 2017).

The defining features of the framework are threefold. First, IBS is informed: it uses admissible estimates of cost-to-come, cost-to-go, and edge cost to prioritize states and edges that may lie on better solutions. Second, it is anytime: it can return an initial feasible solution and then improve that solution as additional computational time yields denser approximation and more focused search. Third, it is asymptotically optimal under appropriate RGG connection conditions: with increasing sample count and properly scaled connectivity, the cost of the solution converges almost surely to the optimum (Gammell et al., 2017).

A central interpretive consequence of this synthesis is that sampling-based planning is no longer viewed merely as random exploration of continuous space. Instead, it is treated as heuristic search over an implicit, progressively refined graph. This suggests that IBS is best understood not as a variant of purely incremental tree growth, but as a queue-driven search procedure over a changing approximation of the continuous planning problem.

2. Formal planning model and notation

The underlying planning problem is the optimal path planning problem in a continuous state space. The state space is

$X \subseteq \mathbb{R}^n,$

with obstacle space

$X_{\mathrm{obs}} \subset X,$

and free space defined as the closure of the obstacle complement,

$$X_{\mathrm{free}} = \mathrm{cl}(X \setminus X_{\mathrm{obs}}).$$

The start state is

$x_{\mathrm{start}} \in X_{\mathrm{free}},$

and the goal region is

$X_{\mathrm{goal}} \subset X_{\mathrm{free}}.$

A path is a continuous, executable, bounded-variation map

$\sigma:[0,1]\to X_{\mathrm{free}},$

with $\Sigma$ denoting the set of all such nontrivial paths. The cost functional is

$c:\Sigma \to \mathbb{R}_{\ge 0},$

and the optimal path is

$$\sigma^* = \arg\min_{\sigma\in\Sigma} c(\sigma) \quad \text{s.t.} \quad \sigma(0)=x_{\mathrm{start}},\; \sigma(1)\in X_{\mathrm{goal}}.$$

IBS adopts the same state and edge cost notation used in the BIT* reconstruction. The explicit search structure is a tree

$X \subseteq \mathbb{R}^n,$0

where $X \subseteq \mathbb{R}^n,$1 and $X \subseteq \mathbb{R}^n,$2. The true cost-to-come through the current tree is denoted $X \subseteq \mathbb{R}^n,$3, with

$X \subseteq \mathbb{R}^n,$4

for states not yet in the tree or unreachable through it. For an edge between $X \subseteq \mathbb{R}^n,$5, the true edge cost is

$X \subseteq \mathbb{R}^n,$6

and

$X \subseteq \mathbb{R}^n,$7

if the edge intersects obstacles.

The heuristic quantities are lower bounds: $X \subseteq \mathbb{R}^n,$8 where $X \subseteq \mathbb{R}^n,$9 is the true optimal cost-to-come, and

$X_{\mathrm{obs}} \subset X,$0

The admissible cost-to-go estimate is $X_{\mathrm{obs}} \subset X,$1, and the combined estimate is

$X_{\mathrm{obs}} \subset X,$2

This notation is significant because it gives IBS a problem-independent baseline description. The framework is not restricted to path length, although path length is the main example in the experiments associated with BIT*.

3. Heuristics, informed subsets, and search ordering

The informed character of IBS is expressed through admissible and, ideally, consistent heuristics. The lower bound on solution cost through a state is

$X_{\mathrm{obs}} \subset X,$3

and the informed subset is

$X_{\mathrm{obs}} \subset X,$4

where $X_{\mathrm{obs}} \subset X,$5 is the cost of the current best solution (Gammell et al., 2017). By definition, this is the set of states that can still participate in a better solution.

Search is ordered through two priority queues. The vertex expansion queue $X_{\mathrm{obs}} \subset X,$6 uses the lexicographic key

$X_{\mathrm{obs}} \subset X,$7

The edge evaluation queue $X_{\mathrm{obs}} \subset X,$8, for a directed edge $X_{\mathrm{obs}} \subset X,$9, uses

$$X_{\mathrm{free}} = \mathrm{cl}(X \setminus X_{\mathrm{obs}}).$$0

These keys implement A*-like ordering over an implicit graph whose edges may not yet have been collision-checked or fully evaluated.

Under consistency, the heuristic lower bounds satisfy

$$X_{\mathrm{free}} = \mathrm{cl}(X \setminus X_{\mathrm{obs}}).$$1

which means that the queue value of a vertex is a lower bound on the value of any of its outgoing edges. This property supports the comparison between the best pending vertex and the best pending edge, allowing the search to decide whether to expand a vertex or evaluate an edge next.

For path-length problems in Euclidean space, $$X_{\mathrm{free}} = \mathrm{cl}(X \setminus X_{\mathrm{obs}}).$$2, $$X_{\mathrm{free}} = \mathrm{cl}(X \setminus X_{\mathrm{obs}}).$$3, and $$X_{\mathrm{free}} = \mathrm{cl}(X \setminus X_{\mathrm{obs}}).$$4 are typically Euclidean distances. In that case, the informed subset becomes an $$X_{\mathrm{free}} = \mathrm{cl}(X \setminus X_{\mathrm{obs}}).$$5 prolate hyperspheroid: $$X_{\mathrm{free}} = \mathrm{cl}(X \setminus X_{\mathrm{obs}}).$$6 Its volume, in the JIT sampling extension, is

$$X_{\mathrm{free}} = \mathrm{cl}(X \setminus X_{\mathrm{obs}}).$$7

where

$$X_{\mathrm{free}} = \mathrm{cl}(X \setminus X_{\mathrm{obs}}).$$8

and

$$X_{\mathrm{free}} = \mathrm{cl}(X \setminus X_{\mathrm{obs}}).$$9

The broader significance is that heuristics in IBS do more than define a post hoc admissible region. They simultaneously restrict the sampled domain, prioritize search order, and filter candidate edges before expensive evaluation. This is a stronger use of heuristic information than sampling restriction alone.

4. Batchwise search on an implicit random geometric graph

IBS uses batches of random samples to define an implicit RGG. For a given batch, the vertex set is formed from the current tree vertices together with sampled states, and edges are defined implicitly either by an $x_{\mathrm{start}} \in X_{\mathrm{free}},$0-disc rule, connecting states within radius $x_{\mathrm{start}} \in X_{\mathrm{free}},$1, or by a $x_{\mathrm{start}} \in X_{\mathrm{free}},$2-nearest rule. The explicit structure maintained by the algorithm is a spanning tree over this graph, while the graph itself is never fully materialized (Gammell et al., 2017).

The algorithmic cycle begins with initialization: $x_{\mathrm{start}} \in X_{\mathrm{free}},$3 The unconnected sample set contains goal states, discretized if necessary, the vertex queue is initialized with the tree vertices, the edge queue is empty, and the current best solution cost is

$x_{\mathrm{start}} \in X_{\mathrm{free}},$4

typically $x_{\mathrm{start}} \in X_{\mathrm{free}},$5 at the outset.

When both queues are empty, a new batch is created. The search first prunes vertices and samples that cannot improve the current solution. It then generates $x_{\mathrm{start}} \in X_{\mathrm{free}},$6 new samples within the informed set,

$x_{\mathrm{start}} \in X_{\mathrm{free}},$7

marks them as new, and resets the vertex queue to contain the current tree vertices. Search within the batch then alternates between vertex expansion and edge processing. Vertices are expanded while the best queue value in $x_{\mathrm{start}} \in X_{\mathrm{free}},$8 is no worse than the best queue value in $x_{\mathrm{start}} \in X_{\mathrm{free}},$9; expansion generates candidate edges through nearest-neighbor queries and inserts only those edges that satisfy heuristic improvement conditions.

Several heuristic filters are applied before true edge evaluation. An edge $X_{\mathrm{goal}} \subset X_{\mathrm{free}}.$0 must satisfy

$X_{\mathrm{goal}} \subset X_{\mathrm{free}}.$1

to be capable of improving the current solution, and

$X_{\mathrm{goal}} \subset X_{\mathrm{free}}.$2

to be capable of improving the tree. Only after these tests is the true edge cost $X_{\mathrm{goal}} \subset X_{\mathrm{free}}.$3 computed and collision checking or boundary-value problem evaluation performed.

This batchwise structure is a core element of IBS. The batch decouples the order in which samples are generated from the order in which they are searched. A large batch makes the procedure resemble A* on a static graph; a batch size of $X_{\mathrm{goal}} \subset X_{\mathrm{free}}.$4 degenerates to a version of RRT* with a steer-free connection scheme. This suggests that batch size is not merely an implementation parameter but a control over the balance between early solution discovery and more globally ordered refinement.

5. Anytime behavior and asymptotic guarantees

IBS is anytime in two distinct senses. It is approximation anytime because the underlying RGG approximation improves as more samples are added and the informed set is refined. It is solution anytime because it can return an initial feasible solution and then continue to seek better solutions through pruning, new batches, and reordered search (Gammell et al., 2017). The sequence of solutions is monotonically improved as more computation is allocated, subject to the heuristics and sampling process.

The formal guarantees are inherited from the BIT* framework. The probabilistic completeness statement is

$X_{\mathrm{goal}} \subset X_{\mathrm{free}}.$5

where $X_{\mathrm{goal}} \subset X_{\mathrm{free}}.$6 is the solution found after $X_{\mathrm{goal}} \subset X_{\mathrm{free}}.$7 samples. Under mild assumptions, a feasible solution is found with probability $X_{\mathrm{goal}} \subset X_{\mathrm{free}}.$8 as $X_{\mathrm{goal}} \subset X_{\mathrm{free}}.$9.

The almost-sure asymptotic optimality statement is

$\sigma:[0,1]\to X_{\mathrm{free}},$0

The key proof idea is that BIT* considers at least the same set of edges as RRT* for equivalent sampling sequences and equivalent connection limits. Since RRT* is asymptotically optimal, the same edge coverage argument supports BIT* and, by extension, the reconstructed IBS baseline.

The RGG conditions are expressed through either a radius threshold or a $\sigma:[0,1]\to X_{\mathrm{free}},$1-nearest threshold. The radius condition is

$\sigma:[0,1]\to X_{\mathrm{free}},$2

with

$\sigma:[0,1]\to X_{\mathrm{free}},$3

and the $\sigma:[0,1]\to X_{\mathrm{free}},$4-nearest condition is

$\sigma:[0,1]\to X_{\mathrm{free}},$5

These conditions are essentially the same scaling laws used in RRT* and PRM*. Their significance for IBS is that the informed search ordering does not replace the need for asymptotically valid graph construction; rather, heuristic ordering and RGG scaling are complementary. Search efficiency depends on the former, while convergence guarantees depend on the latter.

6. Relations to other planners, practical design choices, and limitations

The BIT* experiments compare the method against RRT, RRT-Connect, RRT*, Informed RRT*, BI$\sigma:[0,1]\to X_{\mathrm{free}},$6RRT*, RABIT*, FMT*, and implicit RRG+LPA* variants. In low dimensions, BIT* is reported as competitive with RRT*-type planners and FMT*, while RRT-Connect often returns quick but suboptimal solutions. As dimensionality increases to 4D, 8D, and 16D, BIT* consistently attains a higher probability of solving within time constraints and achieves lower median solution cost, particularly in difficult problems with dual enclosure and many homotopy classes. In 7-DOF and 14-DOF HERB problems, it is reported as the only asymptotically optimal anytime planner that solves all trials within the given times, while finding initial solutions in time comparable to RRT-Connect and producing higher-quality paths (Gammell et al., 2017).

The comparison with Informed RRT* clarifies a recurrent misconception. Informed RRT* focuses sampling to the informed set after a solution is found, but still expands the tree in sampling order; its heuristics do not alter search order before the first solution. BIT*, by contrast, uses heuristics to order search from the beginning and avoids spending effort on samples or states that cannot belong to the best solution in the current graph. This suggests that, within IBS, focusing only the sampling distribution is insufficient if the objective is to make the entire search process informed.

Another important design choice concerns rewiring. BIT* rewires the tree when a new edge improves cost-to-come, but it does not propagate the change to all descendants as LPA* would. The reconstruction characterizes it as closer to TLPA*. This truncated rewiring reduces computational burden while preserving asymptotic optimality. A plausible implication is that IBS can be parameterized between two poles: full propagation for more graph-consistent dynamic shortest-path maintenance, and truncated rewiring for lower overhead.

Practical implementation considerations are similarly explicit. Nearest-neighbor queries dominate runtime and are mitigated by restricting connections through RGG rules and by using efficient data structures such as k-d trees. Edge evaluations are deferred until heuristic tests indicate possible improvement. Pruning removes vertices and samples $\sigma:[0,1]\to X_{\mathrm{free}},$7 for which

$\sigma:[0,1]\to X_{\mathrm{free}},$8

and disconnected vertices inside the informed set may be recycled as new samples in the next batch. The major tunable parameters are batch size $\sigma:[0,1]\to X_{\mathrm{free}},$9, connection radius scaling or $\Sigma$0-nearest threshold, maximum edge length threshold, heuristic choice, and pruning frequency.

No explicit big-$\Sigma$1 complexity analysis is provided. The practical picture is instead heuristic: nearest-neighbor operations and collision checks dominate, while pruning and queue rebuilding add overhead that is necessary to keep the graph focused on states that can still improve the incumbent solution. The resulting framework is therefore best regarded as a baseline architecture for informed continuous planning: an explicit tree searched over an implicit RGG, guided by admissible lower bounds, refined in batches, and supported by asymptotic guarantees.