Cooperative Visual-Inertial Sensor Fusion: Fundamental Equations and State Determination in Closed-Form

Agostino Martinelli 1 Alessandro Renzaglia 1 Alexander Oliva 1
1 CHROMA - Robots coopératifs et adaptés à la présence humaine en environnements dynamiques
CITI - CITI Centre of Innovation in Telecommunications and Integration of services, Inria Grenoble - Rhône-Alpes
Abstract : This paper investigates the visual and inertial sensor fusion problem in the cooperative case and provides new theoretical and basic results.Specifically, the case of two agents is investigated. Each agent is equipped with inertial sensors (accelerometer and gyroscope) and with a monocular camera. By using the monocular camera, each agent can observe the other agent. No additional camera observations (e.g., of external point features in the environment) are considered.First, the entire observable state is analytically derived. This state contains the relative position between the two agents (which includes the absolute scale), the relative velocity, the three Euler angles that express the rotation between the two local frames and all the accelerometer and gyroscope biases.Then, the basic equations that describe this system are analytically obtained. %In other words, both the dynamics of the observable state and all the camera observations are expressed only in terms of the components of the observable state and in terms of the inertial measurements. These are the fundamental equations that fully characterize the problem of fusing visual and inertial data in the cooperative case. The last part of the paper describes the use of these equations to obtain a closed-form solution that provides the observable state in terms of the visual and inertial measurements provided in a short time interval. The impact of the presence of the bias on the performance of this closed-form solution is also investigated and a simple and effective method to obtain the gyroscope bias is proposed.Extensive simulations clearly show that the proposed method is successful. It is worth noting that it is possible to automatically retrieve the absolute scale and simultaneously calibrate the gyroscopes not only without any prior knowledge, but also without external point features in the environment.
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Agostino Martinelli, Alessandro Renzaglia, Alexander Oliva. Cooperative Visual-Inertial Sensor Fusion: Fundamental Equations and State Determination in Closed-Form. Autonomous Robots, Springer Verlag, In press, pp.1-19. ⟨10.1007/s10514-019-09841-8⟩. ⟨hal-02013869⟩

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