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This paper considers the problem of visual-inertial sensor fusion in thecooperative case and it provides new theoretical contributions, which regardits observability and its resolvability in closed form. The case of two agentsis investigated. Each agent is equipped with inertial sensors (accelerometerand gyroscope) and with a monocular camera. By using the monocular camera, eachagent can observe the other agent. No additional camera observations (e.g., ofexternal point features in the environment) are considered. All the inertialsensors are assumed to be affected by a bias. First, the entire observablestate is analytically derived. This state includes the absolute scale, therelative velocity between the two agents, the three Euler angles that expressthe rotation between the two agent frames and all the accelerometer andgyroscope biases. Second, the paper provides the extension of the closed-formsolution given in [19] (which holds for a single agent) to the aforementionedcooperative case. The impact of the presence of the bias on the performance ofthis closed-form solution is investigated. As in the case of a single agent,this performance is significantly sensitive to the presence of a bias on thegyroscope, while, the presence of a bias on the accelerometer is negligible.Finally, a simple and effective method to obtain the gyroscope bias isproposed. Extensive simulations clearly show that the proposed method issuccessful. It is amazing that, it is possible to automatically retrieve theabsolute scale and simultaneously calibrate the gyroscopes not only without anyprior knowledge (as in [13]), but also without external point features in theenvironment.

Closed-form solution to cooperative visual-inertial structure from motion