Transformer architecture has shown significant potential in various visual tasks, including point cloud registration. Positional encoding, as an order-aware module, plays a crucial role in Transformer framework. In this paper, we propose OIF-PCR++, a conditional positional encoding (CPE) method for point cloud registration. The core CPE module utilizes length and vector encoding at different stages, conditioned on the relative pose states between the point clouds to be registered. As a result, it progressively alleviates feature ambiguity through the incorporation of geometric cues. Building upon CPE, we introduce an iterative positional encoding optimization pipeline comprising two stages: 1) We find one correspondence via a differentiable optimal transport layer, and use it to encode length information into point cloud features, enhancing spatial consistency across different reference frames. 2) We apply a progressive direction alignment strategy to achieve rough alignment between paired point clouds, and then gradually incorporate direction information with the aid of this alignment, further enhancing feature distinctiveness and reducing feature ambiguity. Through this iterative optimization process, length and direction information are effectively integrated to achieve consistent and distinctive positional encoding, enabling the learning of discriminative point cloud features. Additionally, we present an inlier propagation mechanism that harmoniously integrates consistent geometric information for positional encoding. The proposed method is highly efficient, introducing marginal computational overhead while significantly improving feature distinguishability. Extensive experiments demonstrate superior performance over state-of-the-art methods on indoor, outdoor, object-level, and multi-way benchmarks, as well as strong generalization to complex real-world scenarios.

Autonomous exploration is a critical challenge for various unmanned aerial vehicle (UAV) applications. Existing methods often suffer from low exploration rates due to limitations such as inefficient global coverage and inadequate sensor data utilization. In this paper, we introduce FIELD, a Fast Information-driven aerial robot Exploration planner using Larger perception Distance. FIELD leverages a larger perception distance to identify high-information-gain viewpoints while maintaining mapping precision and utilizing more sensor data to guide the exploration process. Then, the method incorporates a history-aware coverage path to determine a consistent and reasonable sequence for visiting frontier viewpoints. Local viewpoints are refined to find the optimal combination of these viewpoints. We compare our method with state-of-the-art frontier-based approaches in benchmark environments. Our method significantly improves exploration efficiency by 13% to 17%.