Guaranteed 3D Positioning from Images Boosts Safety of Robots and Autonomous Systems

Researchers are developing methods to guarantee the safety of agents operating in complex cyber-physical systems, a challenge often reliant on accurate pose estimation for subsequent actions. Tobias Ladner from Technical University of Munich, Yasser Shoukry from University of California, Irvine, and Matthias Althoff et al. present a novel certified pose estimation technique in 3D, deriving pose bounds directly from camera imagery and known target geometry. This work is significant because it moves beyond simple pose estimation to formally verify safety, even in worst-case scenarios, without relying on potentially untrustworthy external services. Their approach, leveraging reachability analysis and formal verification, efficiently and accurately localises agents in both simulated and real-world environments, representing a substantial step towards robust and reliable autonomous systems.

This work introduces a method to accurately determine the 3D position and orientation of an agent using only a camera image and knowledge of the target object’s geometry.

Unlike conventional localization techniques that provide approximate estimates, this approach formally bounds the possible poses, guaranteeing a level of certainty essential for safety-critical tasks. The research tackles the limitations of existing methods susceptible to adversarial attacks or unreliable external services like GPS, offering a robust alternative for scenarios demanding formal verification of safety.

The core of this breakthrough lies in leveraging reachability analysis and formal verification to compute a guaranteed range of possible poses from a single camera image. By formally bounding the pose, researchers move beyond probabilistic estimates to provide a certified localization, ensuring safety even in worst-case scenarios.

This is achieved through an innovative application of reachability analysis to enclose the possible images of a target, enabling the retrieval of a certified pose estimate given a concrete image. The approach inherently accounts for uncertainties in pose, camera parameters, and target geometry, enhancing its robustness in real-world conditions.

Experiments demonstrate the efficiency and accuracy of this certified pose estimation in both simulated and real-world environments. Utilising synthetic data and noisy images captured in practical settings, the study showcases tight certified pose estimates, validating the method’s performance. This pure vision-based system, requiring only an event-based camera and known target geometry, such as runway markings or stop signs, represents a significant step towards deploying autonomous agents in safety-critical domains.

The research establishes a foundation for formally verifying the perception of autonomous systems, paving the way for more reliable and trustworthy robotic applications. This certified pose estimation method utilizes a pinhole camera model and defines a target object as a collection of convex polygons within a three-dimensional space.

The system computes the analogue output of the camera by transforming the target’s polygons through rotation, translation, and intrinsic camera parameters, ultimately projecting them onto the image sensor plane. A binary image is then generated, indicating which pixels correspond to the detected target polygons, forming the basis for the subsequent reachability analysis and pose certification. The resulting framework provides a mathematically rigorous approach to localization, crucial for ensuring the safe operation of autonomous agents.

Formal pose estimation via pre-partitioned candidate spaces and reachability analysis

A 72-candidate pose space, denoted as Ξ, was initially partitioned offline, with properties pre-computed for each candidate. Online pose localization was then performed by rapidly and accurately identifying the true pose, ξ∗, within this pre-computed set using two distinct methods. The performance of these methods was evaluated using both synthetic and real-world images, as detailed in Table II, which compares results obtained from raw and cleaned images.

Specifically, the experiments demonstrate that the true pose was consistently contained within the certified pose estimate. The study leveraged reachability analysis and formal verification to formally bound the computed pose. Offline filtering, utilising both an [h] ζ Filter and the presented approach, was compared against a baseline Filter method across three datasets: 30, R, and Stripes.

The [h] ζ Filter achieved times of 5979s, 3966s, and 1405s respectively, with volume percentages of 1.86%, 0.53%, and 0.17%. In contrast, the presented approach achieved times of 41.6±9.3s, 28.5±6.9s, and 30.8±7.2s, with corresponding volume percentages of 0.23±0.08%, 0.12±0.04%, and 0.05±0.02%. Cleaning the images with basic denoising, as shown in Figure 0.9b, substantially reduced online computation time by decreasing the number of candidates considered.

Further analysis involved a standalone experiment on sound image enclosures, demonstrating the tightness of the approach under rotational, zoom, and translational uncertainties. Five random samples were generated from an uncertain pose E, and the resulting transformations were computed. The computed vertices were then assessed for containment within the enclosure VPCF i(·,k), confirming that the samples were spread within the respective set. The average ratio between the interval hull radius of the linearized term and the approximation error was measured to be 18.6%, providing a quantitative measure of outer approximation.

Certified Pose Estimation via Reachability Analysis and Convex Polygon Representation

Certified pose estimates were obtained solely from images and a well-known target geometry, demonstrating a crucial step towards formally guaranteeing safety in autonomous systems. The research successfully encloses possible images of a target using reachability analysis, enabling the retrieval of a certified pose estimate given a concrete image.

This approach naturally incorporates uncertainty in poses, camera parameters, and target geometry, providing robust localization. Synthetic experiments yielded tight certified pose estimates, alongside real-world experiments conducted on noisy images. The work defines a polygon as a convex hull constructed from vertices lying on a plane, described by a plane equation with coefficients c and d.

A target object is then defined as a collection of these convex polygons, all expressed within a target coordinate frame. The image formation process, utilising a pinhole camera model, transforms points from the target coordinate frame through the camera coordinate frame to the final pixel coordinate frame, relying on intrinsic camera parameters like focal length, width, and height, alongside extrinsic pose parameters.

Experiments demonstrate the feasibility of obtaining certified pose estimates in a pure vision-based setting, utilising event-based cameras and known target geometries such as runway markings. The methodology encloses possible images of the target through reachability analysis, allowing for a guaranteed correct perception of the camera’s pose relative to the target.

This is achieved by leveraging formal verification techniques and incorporating uncertainty directly into the pose estimation process. The resulting certified pose estimates were obtained on both synthetic datasets and real-world images, showcasing the approach’s robustness to noise.

Formal verification of three dimensional pose via reachability analysis

Certified pose estimation in three dimensions can be achieved using only camera imagery and prior knowledge of target geometry. This method formally bounds the agent’s pose, utilising reachability analysis and formal verification techniques to guarantee accuracy. Experiments conducted in both simulated and real-world environments demonstrate the efficient and accurate localization of agents relative to a known target within a little over one second.

This research represents a substantial advancement in ensuring the safety of autonomous agents operating in critical applications. By providing a certified pose estimate, the system enables formal safety guarantees, addressing limitations inherent in traditional pose estimation methods that rely on potentially unreliable external services or provide insufficiently precise localizations.

The approach’s reliance on image data and target geometry simplifies the requirements for operation and enhances robustness. The authors acknowledge limitations including the assumption of clear target visibility, the impact of noisy images, and the current focus on single-object scenarios. Future work could address these challenges by improving robustness to adverse weather conditions and malicious manipulation, refining the algorithm for identifying key image features, and extending the method to handle multiple objects simultaneously. Optimisation through implementation in a more efficient programming language and the application of GPU acceleration are also identified as potential avenues for achieving real-time performance.