Consistency-Oriented SLAM Approach: Theoretical Proof and Numerical Validation

Simultaneous Localization and Mapping (SLAM) has long been a fundamental and challenging task in robotics literature, where safety and reliability are the critical issues for successfully autonomous applications of robots. Classically, the SLAM problem is tackled via probabilistic or optimization methods (such as EKF-SLAM, Fast-SLAM, and Graph-SLAM). Despite their strong performance in real-world scenarios, these methods may exhibit inconsistency, which is caused by the inherent characteristic of model linearization or Gaussian noise assumption. In this paper, we propose an alternative monocular SLAM algorithm which theoretically relies on interval analysis (iMonoSLAM), to pursue guaranteed rather than probabilistically defined solutions. We consistently modeled and initialized the SLAM problem with a bounded-error parametric model. The state estimation process is then cast into an Interval Constraint Satisfaction Problem (ICSP) and resolved through interval constraint propagation techniques without any linearization or Gaussian noise assumption. Furthermore, we theoretically prove the obtained consistency and propose a versatile method for numerical validation. To the best of our knowledge, this is the first time such a proof has been proposed. A plethora of numerical experiments are carried to validate the consistency, and a preliminary comparison with classical EKF-SLAM in different noisy situations is also presented. Our proposed iMonoSLAM shows outstanding performance in obtaining reliable solutions, highlighting the potential application prospect in safety-critical scenarios of mobile robots.