Section: New Results

Robust state estimation (Sensor fusion)

1. Exploitation of the closed form solution introduced in [70] in the framework of Micro Aerial Vehicle (MAV) navigation;

2. Introduction of a new method for simultaneous localization and Gyroscope calibration;

3. Analytic solution of the Unknown Input Observability problem (UIO problem) in the nonlinear case.

Regarding the first two topics, we successfully implemented a new method for MAV localization and mapping, on the aerial vehicles available at the Vision and Perception lab at the university of Zurich (This is the partner of the ANR project VIMAD, in charge of the experiments). This method is based on our previous closed form solution recently introduced in [70]. The practical advantage of this solution is that it is able to determine several physical quantities (e.g, speed, orientation, absolute scale) by only using the measurements provided by a monocular camera and an Inertial Measurement Unit (IMU) during a short interval of time (about 3 seconds). In other words, an initialization is not requested to determine the aforementioned physical quantities. This fact has a fundamental importance in robotics and it is novel with respect to all the state of the art approaches for visual-inertial sensor fusion, which use filter-based or optimization-based algorithms. Due to the nonlinearity of the system, a poor initialization can have a dramatic impact on the performance of these estimation methods.

Finally, by further studying the impact of noisy sensors on the performance of the closed-form solution introduced in [70], we found that this performance is very sensitive to the gyroscope bias. For, we developed a powerful and simple optimization approach to remove this bias. This method has been tested in collaboration with the vision and perception team in Zurich (in the framework of the ANR-VIMAD) and published on the IEEE Robotics and Automation Letters [12]. Additionally, these results have been presented at the International Conference on Robotics and Automation [21].

Regarding the third topic, we still considered the problem of deriving the observability properties of the visual-inertial structure from motion problem when the number of inertial sensors is reduced. This case corresponds to solve a problem that in control theory is known as the Unknown Input Observability (UIO). This problem was still unsolved in the nonlinear case. In [71] we introduced a new method able to provide sufficient conditions for the state observability. On the other hand, this method is based on a state augmentation. Specifically, the new extended state includes the original state together with the unknown inputs and their time-derivatives up to a given order. Then, the method introduced in [71] is based on the computation of a codistribution defined in the augmented space. This makes the computation necessary to derive the observability properties dependent on the dimension of the augmented state. Our effort to deal with this fundamental issue, was devoted to separate the information on the original state from the information on its extension. Last year, we fully solved this problem in the case of a single unknown input [73], [72]. This year we solved the problem for any number of unknown inputs. We presented this solution at the university of Pisa in June and at the university of Rome, Tor Vergata, in December.