BOWConnect: Bidirectional Kinodynamic Planner

• The paper introduces BOWConnect, a planner that integrates Bayesian optimization over short control windows with bidirectional tree sampling to generate collision-free, dynamically feasible trajectories.
• It combines local surrogate models with a global exploration framework using spatial hashing and a boundary value solver to efficiently connect forward and backward search trees.
• Experimental evaluations on both ground and aerial platforms show 100% success in complex environments, demonstrating improved sample efficiency and trajectory quality over classic kinodynamic methods.

Searching arXiv for the BOWConnect paper and closely related kinodynamic motion-planning work.

BOWConnect is a bidirectional, parallel kinodynamic motion planner that integrates Bayesian Optimization over Windows (BOW) as a learning-based steering function within a tree-based sampling architecture for generating collision-free, dynamically feasible trajectories in continuous state and control spaces (Raxit et al., 25 Jun 2026). It is designed for planning problems in which motion must satisfy differential constraints, so the relevant search domain is the full state space $\mathbf{x}=(q,\dot q)\in\mathcal{X}$, not merely configuration space. The method is explicitly motivated by three limitations of existing sampling-based kinodynamic planners: sample inefficiency in high-dimensional state spaces, unreliable cost heuristics under dynamic constraints, and poor performance in narrow passage environments (Raxit et al., 25 Jun 2026). In the formulation reported for BOWConnect, multiple forward and backward workers grow trees in parallel from sampled start and goal-region states, while a spatial hashing scheme accelerates connection discovery and a boundary value problem solver produces kinodynamically consistent bridge trajectories (Raxit et al., 25 Jun 2026).

1. Planning setting and design motivation

BOWConnect addresses the kinodynamic motion-planning problem in which trajectories must remain inside the collision-free feasible state space while satisfying system dynamics of the form

$\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$

with admissible controls $\mathbf{u}\in\mathcal{U}\subset\mathbb{R}^m$ (Raxit et al., 25 Jun 2026). The paper defines the configuration space $\mathcal{C}$, the collision-free subset $\mathcal{C}_{\text{free}}$, the state space $\mathcal{X}=T\mathcal{C}$, and the feasible state space

$$\mathcal{X}_{\text{free}} = \{(q,\dot{q}) \in \mathcal{X} \mid q \in \mathcal{C}_{\text{free}}\}.$$

A trajectory over horizon $T$ induced by a control $\mathbf{u}$ is denoted

$$\tau(\mathbf{u}) = \Phi(\mathbf{x}, \mathbf{u}) = \{\mathbf{x}(t) : t \in [0, T]\},$$

and the planning objective is to find a feasible $\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$0 that reaches the goal state (Raxit et al., 25 Jun 2026).

The planner is positioned against classical kinodynamic methods such as RRT, SST, EST, and KPIECE, as well as against the authors’ earlier unidirectional BOW method (Raxit et al., 25 Jun 2026). The central criticism is that many classical planners rely on random control sampling and weak geometric heuristics, whereas geometric proximity is often a poor surrogate for actual transition cost or reachability under nonholonomic and dynamic constraints (Raxit et al., 25 Jun 2026). The paper therefore replaces random local steering with an online learning procedure over short control horizons and embeds it in a global bidirectional exploration framework.

A plausible implication is that BOWConnect is best understood not as a purely local optimizer or a purely global sampling planner, but as a hybrid architecture in which local model-based learning and global tree connectivity are coupled at every stage. The paper’s direct comparison to the earlier BOW planner suggests that the addition of bidirectionality, worker-level parallelism, and explicit connection machinery is intended to remedy the global exploration limitations of a unidirectional windowed Bayesian-optimization planner (Raxit et al., 25 Jun 2026).

2. Bayesian Optimization over Windows as local steering

In BOWConnect, BOW denotes the use of Bayesian optimization over short finite-horizon control windows (Raxit et al., 25 Jun 2026). Rather than optimizing an entire long trajectory globally, the planner optimizes over a local horizon $\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$1, starting from a current state $\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$2, over controls $\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$3, using forward simulation under the dynamics and online surrogate modeling in the control space (Raxit et al., 25 Jun 2026). This local optimizer serves as the planner’s steering function.

The paper defines a local reward

$\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$4

and a feasibility indicator

$\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$5

Two Gaussian process surrogates are then learned: $\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$6 for reward and $\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$7 for feasibility, with predictive moments

$\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$8

The estimated probability of feasibility is

$\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$9

and the constrained acquisition function used to select the next control is

$\mathbf{u}\in\mathcal{U}\subset\mathbb{R}^m$0

The control maximizing $\mathbf{u}\in\mathcal{U}\subset\mathbb{R}^m$1 is used to generate the next short-horizon motion primitive (Raxit et al., 25 Jun 2026).

The paper describes the resulting surrogate models as local cost maps and constraints, but these are not global workspace maps. They are local probabilistic surrogates over controls, encoding which controls are likely to make progress toward the target and which are likely to remain feasible in the current local planning context (Raxit et al., 25 Jun 2026). This distinction is important: the learned object is a local model of the short-horizon reachable structure, not a persistent global value function.

This suggests that the BOW component is effectively a dynamics-aware receding-horizon local planner embedded inside a sampling framework. The article’s terminology of “windows” therefore refers to short planning horizons in time and control space, not to fixed geometric windows in configuration space (Raxit et al., 25 Jun 2026).

3. Bidirectional parallel architecture

BOWConnect is not a single-tree planner. It uses a bidirectional architecture with multiple workers operating in parallel, divided into $\mathbf{u}\in\mathcal{U}\subset\mathbb{R}^m$2 forward workers and $\mathbf{u}\in\mathcal{U}\subset\mathbb{R}^m$3 backward workers (Raxit et al., 25 Jun 2026). The planner first samples multiple start-region states and goal-region states: $\mathbf{u}\in\mathcal{U}\subset\mathbb{R}^m$4

$\mathbf{u}\in\mathcal{U}\subset\mathbb{R}^m$5

These states are collision-free samples within a radius around the start and goal regions, each with a random heading $\mathbf{u}\in\mathcal{U}\subset\mathbb{R}^m$6, which the paper states is important for resolving heading ambiguity at the goal and diversifying exploration (Raxit et al., 25 Jun 2026).

Each worker maintains its own search tree and its own BOW instance (Raxit et al., 25 Jun 2026). Repeatedly, a worker samples a random state $\mathbf{u}\in\mathcal{U}\subset\mathbb{R}^m$7, finds the nearest node $\mathbf{u}\in\mathcal{U}\subset\mathbb{R}^m$8 in its tree, invokes BOW to generate a short-horizon collision-free, dynamically feasible trajectory from $\mathbf{u}\in\mathcal{U}\subset\mathbb{R}^m$9 toward $\mathcal{C}$0, and appends all states along that local trajectory if the attempt succeeds (Raxit et al., 25 Jun 2026).

The main thread performs inter-tree connection checks while workers expand independently. Nearby states from forward and backward trees are detected using spatial hashing, filtered using a kinematic feasibility test, and then passed to a boundary value problem solver to generate a bridge trajectory (Raxit et al., 25 Jun 2026). If a bridge succeeds, the final solution is assembled by merging the forward path, bridge, and backward path. The planner also includes a unidirectional fallback: if a single worker reaches the goal region directly, that solution may be returned (Raxit et al., 25 Jun 2026).

A heuristic explanation for the benefit of many forward/backward workers is given by the idealized expression

$\mathcal{C}$1

where $\mathcal{C}$2 is the success probability of a single forward/backward worker pair (Raxit et al., 25 Jun 2026). The paper does not present this as a completeness theorem, but as an explanation of a portfolio effect due to parallel diversity.

4. Connection machinery: spatial hashing and bridge generation

A central architectural element is the use of spatial hashing to accelerate candidate connection discovery between forward and backward trees (Raxit et al., 25 Jun 2026). Each state is mapped to a discretized grid cell: $\mathcal{C}$3 where $\mathcal{C}$4 is grid resolution, $\mathcal{C}$5 is a reference offset, and $\mathcal{C}$6 denotes bit-packing operations. The paper states that this yields $\mathcal{C}$7 average-case lookup for nearby candidate states (Raxit et al., 25 Jun 2026).

Before invoking a bridge solver, the planner checks a kinematic feasibility condition between a forward-tree state $\mathcal{C}$8 and a backward-tree state $\mathcal{C}$9: $\mathcal{C}_{\text{free}}$0 with

$\mathcal{C}_{\text{free}}$1

Only if this coarse test succeeds does the planner attempt to solve a local connection problem (Raxit et al., 25 Jun 2026).

The bridge trajectory is generated by a boundary value problem solver seeking a control $\mathcal{C}_{\text{free}}$2 such that

$\mathcal{C}_{\text{free}}$3

The reported solver is not an exact analytic steering law. Instead, it uses proportional heading control with heading error

$\mathcal{C}_{\text{free}}$4

and yaw-rate command

$\mathcal{C}_{\text{free}}$5

Forward speed is set proportional to remaining distance, and the resulting bridge is collision checked before acceptance (Raxit et al., 25 Jun 2026).

This structure makes BOWConnect distinct from purely geometric bidirectional planners. The connection phase is not based on straight-line interpolation between states, but on a dynamically consistent local bridge, with hashing and kinematic filtering used to make repeated connection attempts tractable (Raxit et al., 25 Jun 2026).

5. State, control, and system models

The general state representation used by the planner is

$\mathcal{C}_{\text{free}}$6

with robot-specific instantiations given for both ground and aerial vehicles (Raxit et al., 25 Jun 2026).

For the physical unicycle ground-vehicle experiments, the state is

$\mathcal{C}_{\text{free}}$7

with control

$\mathcal{C}_{\text{free}}$8

For the physical quadrotor experiments, the state is

$\mathcal{C}_{\text{free}}$9

with control

$\mathcal{X}=T\mathcal{C}$0

The paper states that fourth-order Runge–Kutta integration is used for forward simulation under the dynamics (Raxit et al., 25 Jun 2026).

Across the benchmark evaluations, the reported planner parameters include speed limits from $\mathcal{X}=T\mathcal{C}$1 to $\mathcal{X}=T\mathcal{C}$2 m/s, maximum acceleration $\mathcal{X}=T\mathcal{C}$3 m/s$\mathcal{X}=T\mathcal{C}$4, maximum yaw rate $\mathcal{X}=T\mathcal{C}$5 rad/s, maximum yaw acceleration $\mathcal{X}=T\mathcal{C}$6 rad/s$\mathcal{X}=T\mathcal{C}$7, time discretization $\mathcal{X}=T\mathcal{C}$8 s, and local planning horizon $\mathcal{X}=T\mathcal{C}$9–$$\mathcal{X}_{\text{free}} = \{(q,\dot{q}) \in \mathcal{X} \mid q \in \mathcal{C}_{\text{free}}\}.$$0 s (Raxit et al., 25 Jun 2026). The planner inputs also include the number of workers $$\mathcal{X}_{\text{free}} = \{(q,\dot{q}) \in \mathcal{X} \mid q \in \mathcal{C}_{\text{free}}\}.$$1, a goal sampling radius $$\mathcal{X}_{\text{free}} = \{(q,\dot{q}) \in \mathcal{X} \mid q \in \mathcal{C}_{\text{free}}\}.$$2, and total time budget $$\mathcal{X}_{\text{free}} = \{(q,\dot{q}) \in \mathcal{X} \mid q \in \mathcal{C}_{\text{free}}\}.$$3 (Raxit et al., 25 Jun 2026).

The global problem statement allows a time-optimal interpretation in which $$\mathcal{X}_{\text{free}} = \{(q,\dot{q}) \in \mathcal{X} \mid q \in \mathcal{C}_{\text{free}}\}.$$4 is minimized over feasible solutions, but the paper does not claim asymptotic optimality for BOWConnect (Raxit et al., 25 Jun 2026). Its stated emphasis is fast feasible planning with high success and favorable trajectory quality.

6. Experimental evaluation

The planner is evaluated on ten benchmark environments: six UGV environments—Bugtrap, Narrow Passage-1, Narrow Passage-2, Forest, Nonconvex, and Intel—and four UAV environments—Quad-1, Quad-2, Quad-3, and Quad-4 (Raxit et al., 25 Jun 2026). Baselines are RRT, SST, EST, KPIECE, and BOW (Raxit et al., 25 Jun 2026). Metrics include planning time, trajectory length, success rate, average velocity, and average jerk (Raxit et al., 25 Jun 2026). UGV planners are tested under both Unicycle and Bicycle motion models (Raxit et al., 25 Jun 2026). The reported hardware platform is Ubuntu 22.04 on an AMD Ryzen 9 7950X with 32 GB RAM, and five trials are run per environment-planner pair (Raxit et al., 25 Jun 2026).

The paper states that BOWConnect achieves 100\% success in all six UGV environments under both Unicycle and Bicycle models (Raxit et al., 25 Jun 2026). In Bugtrap, the reported planning times are $$\mathcal{X}_{\text{free}} = \{(q,\dot{q}) \in \mathcal{X} \mid q \in \mathcal{C}_{\text{free}}\}.$$5 s for Unicycle and $$\mathcal{X}_{\text{free}} = \{(q,\dot{q}) \in \mathcal{X} \mid q \in \mathcal{C}_{\text{free}}\}.$$6 s for Bicycle, both with 100% success (Raxit et al., 25 Jun 2026). In Narrow Passage-1, BOWConnect achieves $$\mathcal{X}_{\text{free}} = \{(q,\dot{q}) \in \mathcal{X} \mid q \in \mathcal{C}_{\text{free}}\}.$$7 s for Unicycle and $$\mathcal{X}_{\text{free}} = \{(q,\dot{q}) \in \mathcal{X} \mid q \in \mathcal{C}_{\text{free}}\}.$$8 s for Bicycle, both with 100% success, whereas the paper reports strong degradation of several baselines under Bicycle dynamics, including 0% success for EST, KPIECE, and BOW (Raxit et al., 25 Jun 2026). In Narrow Passage-2, the corresponding BOWConnect times are $$\mathcal{X}_{\text{free}} = \{(q,\dot{q}) \in \mathcal{X} \mid q \in \mathcal{C}_{\text{free}}\}.$$9 s and $T$0 s, again both with 100% success (Raxit et al., 25 Jun 2026).

In Forest, BOWConnect achieves $T$1 s for Unicycle and $T$2 s for Bicycle, both with 100% success, and the shortest average trajectories among reported methods: $T$3 m for Unicycle and $T$4 m for Bicycle (Raxit et al., 25 Jun 2026). In Nonconvex, it achieves $T$5 s for Unicycle and $T$6 s for Bicycle, again with 100% success, and shortest average trajectories of $T$7 m and $T$8 m, respectively (Raxit et al., 25 Jun 2026). The paper explicitly attributes these shorter paths in Nonconvex to backward-tree guidance (Raxit et al., 25 Jun 2026). In the Intel benchmark, described as the most complex, BOWConnect achieves $T$9 s for Unicycle and $\mathbf{u}$0 s for Bicycle, with 100% success in both cases (Raxit et al., 25 Jun 2026).

For UAV environments, the paper states that all planners achieve 100% success across Quad-1 to Quad-4, but BOWConnect and BOW are much faster than the classical baselines (Raxit et al., 25 Jun 2026). In Quad-1, BOWConnect achieves $\mathbf{u}$1 s with trajectory length $\mathbf{u}$2 m and lowest jerk $\mathbf{u}$3 (Raxit et al., 25 Jun 2026). In Quad-2, it is the fastest method at $\mathbf{u}$4 s (Raxit et al., 25 Jun 2026). In Quad-3, it achieves $\mathbf{u}$5 s (Raxit et al., 25 Jun 2026). In Quad-4, it achieves $\mathbf{u}$6 s, trajectory length $\mathbf{u}$7 m, and lowest jerk $\mathbf{u}$8 (Raxit et al., 25 Jun 2026).

The paper does not include a dedicated ablation table isolating individual components such as spatial hashing or bidirectionality (Raxit et al., 25 Jun 2026). The closest comparison is against the earlier unidirectional BOW planner, which the paper uses to show the effect of adding the bidirectional parallel architecture and connection machinery (Raxit et al., 25 Jun 2026).

7. Real-world deployment

The reported real-world ground platform is an iRobot Create 3 differential-drive educational robot with radius $\mathbf{u}$9 m operating in a $$\tau(\mathbf{u}) = \Phi(\mathbf{x}, \mathbf{u}) = \{\mathbf{x}(t) : t \in [0, T]\},$$0 cluttered indoor laboratory (Raxit et al., 25 Jun 2026). Localization is provided by Vicon motion capture at 120 Hz, and collision checking is performed against a 2D occupancy grid derived from the laboratory layout (Raxit et al., 25 Jun 2026). The planner uses the unicycle motion model, goals are sent interactively via RViz 2D goal commands, maximum linear velocity is $$\tau(\mathbf{u}) = \Phi(\mathbf{x}, \mathbf{u}) = \{\mathbf{x}(t) : t \in [0, T]\},$$1 m/s, maximum angular velocity is $$\tau(\mathbf{u}) = \Phi(\mathbf{x}, \mathbf{u}) = \{\mathbf{x}(t) : t \in [0, T]\},$$2 rad/s, and the low-level control step is $$\tau(\mathbf{u}) = \Phi(\mathbf{x}, \mathbf{u}) = \{\mathbf{x}(t) : t \in [0, T]\},$$3 s (Raxit et al., 25 Jun 2026). The paper reports that feasible trajectories are consistently generated in under $$\tau(\mathbf{u}) = \Phi(\mathbf{x}, \mathbf{u}) = \{\mathbf{x}(t) : t \in [0, T]\},$$4 s, with average planning time $$\tau(\mathbf{u}) = \Phi(\mathbf{x}, \mathbf{u}) = \{\mathbf{x}(t) : t \in [0, T]\},$$5 s, maximum $$\tau(\mathbf{u}) = \Phi(\mathbf{x}, \mathbf{u}) = \{\mathbf{x}(t) : t \in [0, T]\},$$6 s, and no collisions or tracking instabilities across five independent trials (Raxit et al., 25 Jun 2026).

The reported aerial platform is a Parrot Bebop 2 UAV operating in a $$\tau(\mathbf{u}) = \Phi(\mathbf{x}, \mathbf{u}) = \{\mathbf{x}(t) : t \in [0, T]\},$$7 indoor environment containing three box-shaped obstacles: two of size $$\tau(\mathbf{u}) = \Phi(\mathbf{x}, \mathbf{u}) = \{\mathbf{x}(t) : t \in [0, T]\},$$8 m and one of size $$\tau(\mathbf{u}) = \Phi(\mathbf{x}, \mathbf{u}) = \{\mathbf{x}(t) : t \in [0, T]\},$$9 m (Raxit et al., 25 Jun 2026). Goals are sent from RViz using the Nav Goal tool (Raxit et al., 25 Jun 2026). The paper states that planned and executed trajectories align well and that collision-free trajectories are consistently computed in under $\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$00 s (Raxit et al., 25 Jun 2026).

These deployments are used as evidence that the planner can operate in real time on both a ground vehicle and a quadrotor under the state and control models described above (Raxit et al., 25 Jun 2026).

8. Interpretation, significance, and limitations

BOWConnect’s central methodological claim is that learned local cost and feasibility models improve sample efficiency, while parallel bidirectional exploration improves global connectivity, especially in narrow passages and non-convex spaces (Raxit et al., 25 Jun 2026). The acquisition function

$\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$01

is the mechanism by which the local planner balances progress toward the target against estimated collision risk (Raxit et al., 25 Jun 2026). The paper’s explanation of narrow-passage behavior is that repeated collisions reduce the feasibility-weighted score of controls heading directly into obstacles, causing the optimizer to shift toward controls that remain inside free space (Raxit et al., 25 Jun 2026).

The planner is also presented as a practical way to make bidirectional kinodynamic planning effective despite the absence of an exact two-point steering function (Raxit et al., 25 Jun 2026). In this respect, the bridge solver and hashing-based connection layer are as central to the method as the local Bayesian optimization component.

Several limitations are either stated or implied. The bridge solver is heuristic rather than exact, relying on proportional control rather than an analytic kinodynamic steering solution (Raxit et al., 25 Jun 2026). Actual parallel speedup is limited by connection checking overhead and sequential BVP solving (Raxit et al., 25 Jun 2026). The current scope is static environments, with dynamic obstacles identified as future work, and planning under uncertainty is likewise listed as future work (Raxit et al., 25 Jun 2026). The paper does not provide asymptotic optimality or strong formal completeness guarantees specific to BOWConnect (Raxit et al., 25 Jun 2026). It also omits several lower-level implementation details, including kernel choice, GP hyperparameter fitting procedure, number of BO iterations per window, exact acquisition optimizer, exact worker count used in benchmarks, and exact hash resolution $\dot{\mathbf{x}} = f(\mathbf{x}, \mathbf{u}),$02 (Raxit et al., 25 Jun 2026).

A common misconception would be to interpret BOWConnect as merely a parallelized version of BOW or a kinodynamic analogue of RRT-Connect. The paper argues for a more specific characterization: BOWConnect is a planner in which online constrained Bayesian optimization over short windows is the local steering primitive, bidirectional parallel search supplies global exploration and connection opportunities, spatial hashing supplies efficient cross-tree candidate discovery, and a BVP solver enforces kinodynamic consistency at the connection stage (Raxit et al., 25 Jun 2026).

9. Position within related motion-planning work

The paper situates BOWConnect relative to classical kinodynamic planners such as RRT, EST, KPIECE, and SST, which it characterizes as being heavily dependent on random control sampling and weak geometric heuristics (Raxit et al., 25 Jun 2026). It also positions itself relative to prior BO-based or GP-based planners, describing them as data efficient but typically computationally expensive and often limited to unidirectional or locally greedy use (Raxit et al., 25 Jun 2026). Compared with the earlier BOW planner, BOWConnect adds bidirectional search, multiple forward and backward workers, tree-based exploration, spatial-hash-assisted connection discovery, and BVP bridge creation (Raxit et al., 25 Jun 2026).

This suggests that BOWConnect should be regarded as an integration of several distinct strands of planning methodology: model-based local optimization over controls, tree-based kinodynamic exploration, multithreaded search diversification, and approximate boundary-value connection methods. The closest antecedent identified by the paper is its own earlier unidirectional BOW framework, but the architectural scope of BOWConnect is substantially broader (Raxit et al., 25 Jun 2026).

The paper states that videos of real-world and simulated experiments, high-resolution figures, and open-source code are available at the project site, indicating an emphasis on practical reproducibility as well as algorithmic novelty (Raxit et al., 25 Jun 2026).