Optimal camera-robot pose estimation in linear time from points and lines

Abstract: Camera pose estimation is a fundamental problem in robotics. This paper focuses on two issues of interest: First, point and line features have complementary advantages, and it is of great value to design a uniform algorithm that can fuse them effectively; Second, with the development of modern front-end techniques, a large number of features can exist in a single image, which presents a potential for highly accurate robot pose estimation. With these observations, we propose AOPnP(L), an optimal linear-time camera-robot pose estimation algorithm from points and lines. Specifically, we represent a line with two distinct points on it and unify the noise model for point and line measurements where noises are added to 2D points in the image. By utilizing Plucker coordinates for line parameterization, we formulate a maximum likelihood (ML) problem for combined point and line measurements. To optimally solve the ML problem, AOPnP(L) adopts a two-step estimation scheme. In the first step, a consistent estimate that can converge to the true pose is devised by virtue of bias elimination. In the second step, a single Gauss-Newton iteration is executed to refine the initial estimate. AOPnP(L) features theoretical optimality in the sense that its mean squared error converges to the Cramer-Rao lower bound. Moreover, it owns a linear time complexity. These properties make it well-suited for precision-demanding and real-time robot pose estimation. Extensive experiments are conducted to validate our theoretical developments and demonstrate the superiority of AOPnP(L) in both static localization and dynamic odometry systems.

• The paper introduces AOPnP(L), an algorithm that integrates point and line measurements to achieve CRB-optimal pose estimation in linear time.
• It employs a two-step scheme with bias elimination followed by a Gauss-Newton refinement to ensure statistical efficiency.
• Experimental results on synthetic and real-world datasets demonstrate superior accuracy and robustness over existing methods.

Optimal Camera-Robot Pose Estimation in Linear Time from Points and Lines

Introduction

The paper presents a novel approach to camera-robot pose estimation, leveraging both point and line features from images for more robust and precise localization. This fusion of complementary features is crucial for enhancing accuracy, particularly in scenarios where one feature type might be inadequate. The paper introduces an algorithm named AOPnP(L) which is theoretically optimal, achieving the Cramér-Rao lower bound (CRB) for estimation accuracy and possessing linear time complexity, making it suitable for real-time applications.

Core Contributions

1. Unified Noise Model and Line Representation: The algorithm represents 3D lines using Plücker coordinates and models both point and line measurement noises as Gaussian noise added to 2D projections. The unified residual formulation allows the combined use of point and line measurements in a maximum likelihood (ML) framework.
2. Two-Step Estimation Scheme:
   • Step 1: A consistent pose estimate is derived by bias elimination from a generalized trust region subproblem (GTRS).
   • Step 2: A single Gauss-Newton (GN) iteration refines this initial estimate, achieving the CRB, thus ensuring asymptotic efficiency.
3. Practical Estimator Modules: The algorithm incorporates robust preprocessing steps for data normalization and a consistent noise variance estimation module, enhancing numerical stability and adapting to unknown noise characteristics.
4. Extensive Validation: Through both synthetic and real-world experiments, the algorithm demonstrates superior performance in static localization and dynamic odometry systems, consistently achieving lower estimation errors than state-of-the-art methods.

Theoretical Framework

The paper's theoretical foundation is built on several key areas:

• DLT and GTRS Relaxation: The underlying problem formulates as a DLT problem, then relaxed to a GTRS for theoretical tractability. The bias elimination ensures consistency by accurately modeling the statistical properties of the noise.
• CRB and Asymptotic Efficiency: By ensuring that the pose estimate refines to the theoretical lower bound via CRB, the paper guarantees that the derived estimates are not only unbiased but also minimize variance.

Algorithm Design

Step 1: Consistent Estimate

• Initial Estimation: Points and lines are normalized based on camera intrinsic parameters, ensuring numerical stability during optimization.
• Noise Variance Estimation: A generalized eigenvalue problem provides a consistent estimate of noise variance. This estimate is crucial for bias elimination.
• Bias Elimination: The consistent pose estimates are generated by solving the bias-eliminated GTRS, ensuring convergence to the true pose.

Step 2: Gauss-Newton Iteration

• Refinement: A single GN iteration is applied using the initial estimate, treating the rotation as a Lie group over SO(3). This step ensures that the refined pose estimate achieves the CRB, guaranteeing optimal accuracy.

Experimental Validation

Synthetic Data

• Noise Models: Various noise levels and feature combinations were tested, demonstrating that the proposed algorithm outperforms existing methods in terms of MSE and bias reduction.
• Consistency and Efficiency: The asymptotic properties and linear complexity were validated. The algorithm maintains computational efficiency, crucial for real-time applications.

Real-World Data

• Static Localization: Using datasets like ETH3D and VGG, the algorithm showed superior performance in estimating the camera's position and orientation, often surpassing existing methods in both accuracy and robustness.
• Dynamic Odometry: Implementing the algorithm in a stereo visual odometry pipeline demonstrated its applicability and reliability in real-time navigation scenarios, showcasing lower absolute pose errors compared to other state-of-the-art PnP solvers.

Implications and Future Work

The proposed AOPnP(L) algorithm sets a new standard for camera-robot pose estimation by combining theoretical optimality with practical applicability. The fusion of point and line features within a unified ML framework offers enhanced robustness across diverse environments. Future directions point to exploring more concise parameterizations to further reduce computational footprint and extend applicability to broader robotic navigation contexts, including outlier-prone scenarios where robust estimation is paramount.

Conclusion

This paper makes significant strides in camera-robot pose estimation by effectively integrating complementary visual features and leveraging advanced statistical techniques to ensure both high precision and computational efficiency. The adaptability and robustness of the AOPnP(L) algorithm mark it as a vital tool for precision-demanding and real-time robotic applications, paving the way for more resilient and accurate robotic navigation systems.