Global Key Points Prediction Network

• The paper introduces GKPN as a predictor of ordered sparse 3D key points from a single depth image and 3D goal, enabling global guidance for hybrid land–air navigation.
• The network employs a two-stage framework where a Sobel-enhanced perception module (SPN) and a lightweight attention planning network (LAPN) collaboratively reduce computational cost while preserving structure.
• Empirical results demonstrate improved goal reachability and energy efficiency, supporting real-time, CPU-only deployment across diverse scenarios.

Searching arXiv for the specified GKPN paper and closely related navigation work to ground the article. Global Key Points Prediction Network (GKPN) is the learning component of a two-stage lightweight framework for autonomous navigation of land–air bimodal robots (LABRs). In this formulation, GKPN predicts an ordered sparse set of 3D key points from a single depth image and a 3D goal, thereby providing global guidance for a hybrid land–air path, while a mapping-based planner refines the key-point sequence into a smooth, collision-free local trajectory (Li et al., 30 Jul 2025). The design targets a setting in which the robot must reach a goal in $S \subset \mathbb{R}^3$, avoid obstacles $S_{obs} \subset S$, remain dynamically feasible during land–air transitions, and minimize energy consumption by favoring ground motion whenever possible. A central characteristic of the method is the division of labor between learned global intent and mapping-based local safety, which the source presents as a response to the conservatism of purely mapping-based planning and the computational and safety limitations of purely learning-based navigation (Li et al., 30 Jul 2025).

1. System definition and operational role

GKPN is defined as a predictor of global key points for hybrid navigation. At time $t$, it takes a depth image $D_t \in \mathbb{R}^{W \times H}$ and a goal position $p_t^G \in \mathbb{R}^3$, and outputs an ordered set of $n$ global key points,

$$K_t = \mathrm{GKPN}(D_t, p_t^G; \theta) \in \mathbb{R}^{n \times 3},$$

where each key point is a 3D coordinate in the robot’s frame or scene coordinates (Li et al., 30 Jul 2025). These key points delineate a hybrid land–air path: segments near ground height imply terrestrial traversal, whereas elevated segments imply flight.

The network operates as the first stage of a two-stage framework. In Stage 1, GKPN predicts a sparse path that implicitly allocates land and air motion. In Stage 2, the global key point sequence is segmented into local subgoals, and a mapping-based local planner refines each segment into a smooth, collision-free trajectory within the local planning horizon (Li et al., 30 Jul 2025). This architecture is intended to preserve the long-range intent supplied by learning while relying on local mapping for geometric precision and collision checking.

A plausible implication is that GKPN should be understood less as a complete end-to-end controller than as a global structural prior over feasible hybrid motion. The source emphasizes this point by attributing final local safety and precision to the second-stage planner rather than to the network alone (Li et al., 30 Jul 2025).

2. Input representation, preprocessing, and architectural composition

GKPN uses the current single depth image and the 3D goal as inputs. The depth data are provided by an Intel RealSense D435i RGB-D camera, and an onboard IMU is fused with the camera via VSLAM for visual–inertial state estimation; however, GKPN itself consumes only the current depth frame $D_t$ and the goal $p_t^G$ (Li et al., 30 Jul 2025). No occupancy map or height map is required by the network.

The architecture consists of two named components: the Sobel Perception Network (SPN) and the Lightweight Attention Planning Network (LAPN). SPN augments raw depth with edge information, motivated by the observation that depth images can be weak on edge and shape cues when gradients are smooth. It uses a two-branch feature extractor: one branch applies a standard CNN to $D_t$, and the other applies Sobel convolution followed by convolution and pooling. The resulting features are concatenated and fused with a residual block,

$S_{obs} \subset S$0

The paper states that SPN applies “Sobel convolution” but does not list kernels; the detailed summary notes that standard horizontal and vertical Sobel filters are used in practice, while also marking that kernel specification is not explicitly printed in the paper (Li et al., 30 Jul 2025).

LAPN performs efficient goal-conditioned feature fusion and key-point decoding. The goal is first embedded into a higher-dimensional representation $S_{obs} \subset S$1 through a linear layer, while the perception features are dimension-matched by another linear layer. LAPN then computes feature weights from the goal embedding and applies them to the perception features:

$S_{obs} \subset S$2

$S_{obs} \subset S$3

The reweighted features are concatenated with the goal embedding and decoded into key points,

$S_{obs} \subset S$4

$S_{obs} \subset S$5

with $S_{obs} \subset S$6 denoting ReLU (Li et al., 30 Jul 2025).

Component	Function	Reported effect
SPN	Fuses raw depth and Sobel edge features	Improves obstacle boundary perception
LAPN	Goal-conditioned lightweight feature reweighting	Reduces cost relative to quadratic attention
GKPN output head	Predicts ordered 3D key points	Supplies sparse hybrid land–air path

The paper also states that GKPN predicts a scalar collision probability $S_{obs} \subset S$7 for the resulting trajectory during training, and that this value is used in the fear loss and to screen unsafe outputs at deployment (Li et al., 30 Jul 2025).

3. Lightweight attention mechanism and efficiency profile

A defining property of GKPN is that LAPN replaces quadratic-cost attention with linear feature reweighting driven by the goal embedding. The source contrasts this with conventional self-attention that uses explicit $S_{obs} \subset S$8, $S_{obs} \subset S$9, and $t$0 projections and an $t$1 softmax$t$2 interaction. LAPN instead uses a single linear map to produce weights from the goal and a linear map for features, yielding $t$3 complexity in the feature dimensionality (Li et al., 30 Jul 2025).

The efficiency claims in the source are explicit. Relative to the iPlanner baseline, the combined SPN+LAPN configuration has 47.7M parameters and 17.8 GFLOPs, compared with 54.3M parameters and 20.64 GFLOPs for iPlanner. The summary reports this as a 14% reduction in parameters and a 13.8% reduction in FLOPs (Li et al., 30 Jul 2025). Additional ablation figures are also given: “Only LAPN” has 45.6M parameters and 16.75 GFLOPs, while “Only SPN” has 53.2M parameters and 21.12 GFLOPs (Li et al., 30 Jul 2025).

These numbers locate LAPN as the principal source of computational reduction. SPN, by contrast, is not primarily an efficiency module; its stated role is to improve obstacle detection by sharpening edge and contour information in depth imagery (Li et al., 30 Jul 2025). This suggests that the architecture partitions responsibilities cleanly: SPN improves perceptual discrimination, whereas LAPN improves global conditioning and computational tractability.

The framework is reported to achieve real-time navigation without GPU acceleration and to support zero-shot transfer from simulation to reality on a CPU-only onboard computer (Li et al., 30 Jul 2025). Specific frequency or latency figures are not reported.

4. Training objective, trajectory construction, and safety signal

During training, GKPN’s key points are converted into a denser trajectory representation by cubic-spline interpolation. If $t$4 intermediate points are inserted between consecutive key points, the resulting trajectory is

$t$5

This interpolated trajectory is used to compute differentiable costs and the fear loss, with gradients flowing back through the spline and the network (Li et al., 30 Jul 2025).

The overall objective is

$t$6

The trajectory cost is

$t$7

where $t$8 is obstacle loss, $t$9 is motion smoothness loss, $D_t \in \mathbb{R}^{W \times H}$0 is goal reachability loss, and $D_t \in \mathbb{R}^{W \times H}$1 is energy loss (Li et al., 30 Jul 2025). The source states that obstacle and smoothness losses follow iPlanner, as differentiable collision proximity and smoothness measures, but it does not reproduce their analytical forms.

The goal reachability term uses a conditional rule that measures either planar or full 3D discrepancy depending on whether the goal lies below robot height $D_t \in \mathbb{R}^{W \times H}$2:

$D_t \in \mathbb{R}^{W \times H}$3

$D_t \in \mathbb{R}^{W \times H}$4

This formulation explicitly favors 2D convergence when the goal is below robot height, thereby encouraging ground navigation when feasible (Li et al., 30 Jul 2025).

The energy term penalizes vertical deviation from the robot’s ground height,

$D_t \in \mathbb{R}^{W \times H}$5

This discourages unnecessary flight and vertical excursions (Li et al., 30 Jul 2025). The summary interprets this as the training-time proxy for energy, while noting that the paper reports real-world energy in Joules without giving an analytical power model.

Safety is further mediated by the fear loss. GKPN predicts a collision probability $D_t \in \mathbb{R}^{W \times H}$6, and the loss is defined by binary cross-entropy:

$D_t \in \mathbb{R}^{W \times H}$7

At deployment, only plans with $D_t \in \mathbb{R}^{W \times H}$8 are accepted (Li et al., 30 Jul 2025). This arrangement separates geometric refinement from safety screening: the second-stage planner enforces local feasibility, while GKPN also learns a coarse unsafe/safe discriminator over its own predicted trajectories.

5. Integration with local planning and hybrid mode selection

The second stage of the framework uses the global key points as segment boundaries for a mapping-based local planner. Each adjacent key-point pair defines a local segment, and Ego-planner refines that segment within its local map or planning horizon into a smooth, collision-free, dynamically feasible trajectory (Li et al., 30 Jul 2025). The paper describes Ego-planner as an ESDF-free, gradient-based local planner, but does not provide its analytic cost function.

In training, cubic splines are used to interpolate between key points. In deployment, interpolation and collision checking are carried out by the local planner using the latest local map, which the summary presents as a mechanism for reducing risk from perceptual blind spots (Li et al., 30 Jul 2025). This is important because GKPN itself uses only a single depth image and does not maintain an explicit occupancy representation.

Hybrid land–air switching is induced rather than explicitly classified. The source states that GKPN tends to place key points near the ground unless the goal height requires flight, due to the combined effect of $D_t \in \mathbb{R}^{W \times H}$9 and the conditional form of $p_t^G \in \mathbb{R}^3$0 (Li et al., 30 Jul 2025). In practice, the robot remains in ground mode while key points remain near $p_t^G \in \mathbb{R}^3$1 and only switches to flight when a key point is sufficiently elevated and spatially close to the goal.

This suggests that the framework implements mode selection through geometric structure in the predicted path rather than through a separate discrete decision head. Such an arrangement is consistent with the article’s emphasis on sparse path prediction as the learned global representation (Li et al., 30 Jul 2025).

6. Empirical results, deployment characteristics, and limitations

The reported training data consist of approximately 20k depth images from the iPlanner dataset, with scenes from Matterport3D and Gazebo-simulated campus and tunnel environments (Li et al., 30 Jul 2025). To move beyond planar navigation, the authors randomly perturb goal heights during training so that targets appear on the ground or in the air. Four simulated environments are used for evaluation: indoor, garage, forest, and a Matterport3D room, with success defined as reaching within 0.5 m of the goal over 100 trials per environment (Li et al., 30 Jul 2025).

The ablation results attribute gains to both SPN and LAPN. In Matterport3D, goal reached rate and training loss progress from baseline 64% (3.671), to LAPN only 68% (3.542), to SPN only 72% (3.320), to SPN+LAPN 76% (3.221). In the indoor setting, the sequence is 86% (1.588), 84% (1.457), 88% (1.523), and 91% (1.322). In the garage setting, it is 95% (0.679), 94% (0.723), 95% (0.665), and 96% (0.632). In the forest setting, it is 94% (0.664), 94% (0.645), 95% (0.642), and 96% (0.636) (Li et al., 30 Jul 2025). The summary identifies SPN as particularly helpful in obstacle-dense indoor and Matterport3D scenes, while LAPN improves long-range, goal-conditioned context.

Real-world results are also reported for CPU-only deployment. In land navigation, the two-stage method achieves 11.8 s and 1008.7 J, compared with Ego-planner at 19.2 s and 1544.41 J and iPlanner at 13.7 s and 1161.44 J (Li et al., 30 Jul 2025). In land–air navigation, the framework is reported to reduce aerial distance by 4.4 m and total energy by 35% compared with the mapping-based baseline, with Ego-planner at 3.2 m land / 5.8 m air / 17225.8 J and the proposed method at 7.2 m land / 1.4 m air / 11010.7 J (Li et al., 30 Jul 2025). The source also states that iPlanner cannot handle air goals.

The deployment stack uses a GPU-free onboard NUC-class CPU computer, a D435i RGB-D camera, an IMU for VSLAM, a Pixhawk flight controller, and an STM32 land controller (Li et al., 30 Jul 2025). Zero-shot sim-to-real transfer is explicitly reported.

Several limitations and omissions are equally explicit. The paper does not state code availability. Although it says that training aligns with iPlanner’s setup for fair comparison, optimizer, learning rate, batch size, epochs, and random seeds are not specified (Li et al., 30 Jul 2025). The source also notes a practical systems issue: on actual hardware without GPU acceleration, camera processing latency required a reduced key-point transmission rate to keep the controller synchronized, which can slow navigation (Li et al., 30 Jul 2025). Detailed sensitivity analyses and negative cases beyond these observations are not reported.

A common misconception would be to treat GKPN as identical to the grasp-detection model GKNet. The two are distinct despite acronymal similarity: GKNet addresses paired keypoint prediction for robotic grasp detection in image space (Xu et al., 2021), whereas GKPN addresses sparse 3D key-point prediction for land–air navigation within a two-stage planner (Li et al., 30 Jul 2025). The overlap is nominal rather than methodological.