No Arabic abstract
The design of navigation observers able to simultaneously estimate the position, linear velocity and orientation of a vehicle in a three-dimensional space is crucial in many robotics and aerospace applications. This problem was mainly dealt with using the extended Kalman filter and its variants which proved to be instrumental in many practical applications. Although practically efficient, the lack of strong stability guarantees of these algorithms motivated the emergence of a new class of geometric navigation observers relying on Riemannian geometry tools, leading to provable strong stability properties. The objective of this brief tutorial is to provide an overview of the existing estimation schemes, as well as some recently developed geometric nonlinear observers, for autonomous navigation systems relying on inertial measurement unit (IMU) and landmark measurements.
This paper deals with the simultaneous estimation of the attitude, position and linear velocity for vision-aided inertial navigation systems. We propose a nonlinear observer on $SO(3)times mathbb{R}^{15}$ relying on body-frame acceleration, angular velocity and (stereo or monocular) bearing measurements of some landmarks that are constant and known in the inertial frame. Unlike the existing local Kalman-type observers, our proposed nonlinear observer guarantees almost global asymptotic stability and local exponential stability. A detailed uniform observability analysis has been conducted and sufficient conditions are derived. Moreover, a hybrid version of the proposed observer is provided to handle the intermittent nature of the measurements in practical applications. Simulation and experimental results are provided to illustrate the effectiveness of the proposed state observer.
This paper considers the problem of attitude, position and linear velocity estimation for rigid body systems relying on landmark measurements. We propose two hybrid nonlinear observers on the matrix Lie group $SE_2(3)$, leading to global exponential stability. The first observer relies on fixed gains, while the second one uses variable gains depending on the solution of a continuous Riccati equation (CRE). These observers are then extended to handle biased angular velocity measurements. Both simulation and experimental results are presented to illustrate the performance of the proposed observers.
This paper considers the problem of simultaneous estimation of the attitude, position and linear velocity for vehicles navigating in a three-dimensional space. We propose two types of hybrid nonlinear observers using continuous angular velocity and linear acceleration measurements as well as intermittent landmark position measurements. The first type relies on a fixed-gain design approach based on an infinite-dimensional optimization, while the second one relies on a variable-gain design approach based on a continuous-discrete Riccati equation. For each case, we provide two different observers with and without the estimation of the gravity vector. The proposed observers are shown to be exponentially stable with a large domain of attraction. Simulation and experimental results are presented to illustrate the performance of the proposed observers.
This paper introduces a novel model-free approach to synthesize virtual sensors for the estimation of dynamical quantities that are unmeasurable at runtime but are available for design purposes on test benches. After collecting a dataset of measurements of such quantities, together with other variables that are also available during on-line operations, the virtual sensor is obtained using machine learning techniques by training a predictor whose inputs are the measured variables and the features extracted by a bank of linear observers fed with the same measures. The approach is applicable to infer the value of quantities such as physical states and other time-varying parameters that affect the dynamics of the system. The proposed virtual sensor architecture - whose structure can be related to the Multiple Model Adaptive Estimation framework - is conceived to keep computational and memory requirements as low as possible, so that it can be efficiently implemented in embedded hardware platforms. The effectiveness of the approach is shown in different numerical examples, involving the estimation of the scheduling parameter of a nonlinear parameter-varying system, the reconstruction of the mode of a switching linear system, and the estimation of the state of charge (SoC) of a lithium-ion battery.
This work considers the problem of resilient consensus where stochastic values of trust between agents are available. Specifically, we derive a unified mathematical framework to characterize convergence, deviation of the consensus from the true consensus value, and expected convergence rate, when there exists additional information of trust between agents. We show that under certain conditions on the stochastic trust values and consensus protocol: 1) almost sure convergence to a common limit value is possible even when malicious agents constitute more than half of the network connectivity, 2) the deviation of the converged limit, from the case where there is no attack, i.e., the true consensus value, can be bounded with probability that approaches 1 exponentially, and 3) correct classification of malicious and legitimate agents can be attained in finite time almost surely. Further, the expected convergence rate decays exponentially with the quality of the trust observations between agents.