Pedro Lourenço

Preliminary results on globally asymptotically stable simultaneous localization and mapping in 3-D

This paper presents the design, analysis, performance evaluation, and preliminary experimental validation of a globally asymptotically stable (GAS) filter for simultaneous localization and mapping (SLAM) with application to unmanned aerial vehicles (UAVs). The SLAM problem is formulated in a sensor-based framework and modified in such a way that the system structure may be regarded as linear time-varying for observability purposes, from which a Kalman filter with GAS error dynamics follows naturally. The proposed solution includes the estimation of both body-fixed linear velocity and rate-gyro measurement biases. Both simulation results and preliminary experimental results, using an instrumented quadrotor equipped with a RGB-D camera, are included in the paper to illustrate the performance of the algorithm under realistic conditions.

Simultaneous localization and mapping for aerial vehicles: a 3-D sensor-based GAS filter

This paper presents the design, analysis, and experimental validation of a globally asymptotically stable (GAS) filter for simultaneous localization and mapping (SLAM) with application to unmanned aerial vehicles. The main contributions of this paper are the results of global convergence and stability for SLAM in tridimensional (3-D) environments. The SLAM problem is formulated in a sensor-based framework and modified in such a way that the structure may be regarded as linear time-varying for observability purposes, from which a Kalman filter with GAS error dynamics follows naturally. The proposed solution includes the estimation of both body-fixed linear velocity and rate gyro measurement biases. Experimental results from several runs, using an instrumented quadrotor equipped with a RGB-D camera, are included in the paper to illustrate the performance of the algorithm under realistic conditions.

Sensor-based globally exponentially stable range-only simultaneous localization and mapping

This paper proposes the design, analysis, and validation of a globally exponentially stable (GES) filter for tridimensional (3-D) range-only simultaneous localization and mapping. For observability analysis purposes, a nonlinear sensor-based dynamical system is formulated resorting only to exact linear and angular kinematics and a state augmentation is exploited that allows the proposed formulation to be considered as linear time-varying without linearizing the original nonlinear system. Constructive observability results can then be established, leading naturally to the design of a Kalman Filter with GES error dynamics. These results also provide valuable insight on the motion planning of the vehicle. Experimental results demonstrate the good performance of the algorithm and help validate the theoretical results presented. For completeness and to illustrate the necessity of a proper trajectory, simulation data are included as well. A novel filter for range-only SLAM is proposed.Sensor-based formulation of SLAM and state augmentation allow LTV Kalman filtering.The error dynamics of the filter are globally exponentially stable.Global convergence of undelayed initial guesses is guaranteed.

Uncertainty characterization of the orthogonal Procrustes problem with arbitrary covariance matrices

Abstract This paper addresses the weighted orthogonal Procrustes problem of matching stochastically perturbed point clouds, formulated as an optimization problem with a closed-form solution. A novel uncertainty characterization of the solution of this problem is proposed resorting to perturbation theory concepts, which admits arbitrary transformations between point clouds and individual covariance and cross-covariance matrices for the points of each cloud. The method is thoroughly validated through extensive Monte Carlo simulations, and particularly interesting cases where nonlinearities may arise are further analyzed.

A received signal strength indication-based localization system

Localization using the received signal strength indication (RSSI) of wireless local area networks with a priori knowledge of the coordinates of the routers/access points is addressed in this paper. The proposed algorithm employs a path loss model that allows for the inclusion of the logarithmic measurements of the signal strength directly in the state of the nonlinear system that is designed. The nonlinear system is augmented in such a way that the resulting system structure may be regarded as linear time-varying for observability purposes, from which a Kalman filter follows naturally. Simulation results are included that illustrate the performance of the proposed solution.

Sensor-based globally asymptotically stable range-only simultaneous localization and mapping

Range-only simultaneous localization and mapping is addressed in this paper, through the design, analysis, and experimental validation of a globally asymptotically stable (GAS) filter. A nonlinear sensor-based system is designed and its dynamics augmented so that the proposed formulation can be considered as linear time-varying for the purpose of observability analysis. This allows the establishment of observability results related to the original nonlinear system that naturally lead to the design of a Kalman filter with GAS error dynamics. The performance of the proposed algorithm is assessed resorting to a set of realistic simulations and to the results obtained from experimental tests.

A globally exponentially stable filter for bearing-only simultaneous localization and mapping in 3-D

This paper proposes a novel filter for sensor-based bearing-only simultaneous localization and mapping in three dimensions with globally exponentially stable (GES) error dynamics. A nonlinear system is designed, its output transformed, and its dynamics augmented so that the proposed formulation can be considered as linear time-varying for the purpose of observability analysis. This allows the establishment of observability results related to the original nonlinear system that naturally lead to the design of a Kalman filter with GES error dynamics. The performance of the proposed algorithm is assessed resorting to a set of realistic simulations.

Simultaneous Localization and mapping in sensor networks: A GES sensor-based filter with moving object tracking

This paper presents the design, analysis, and validation of a globally exponentially stable (GES) filter for tridimensional (3-D) range-only simultaneous localization and mapping in sensor networks with moving object tracking. For observability analysis purposes, two nonlinear sensor-based dynamic systems are formulated resorting only to exact linear and angular kinematics and a motion model for the target. A state augmentation is exploited that allows the proposed formulation to be considered as linear time-varying without linearizing the original nonlinear systems. Constructive observability results can then be established, leading naturally to the design of a Kalman Filter with GES error dynamics. These results also provide valuable insight on the motion planning of the vehicle. Simulation results demonstrate the good performance of the algorithm and help validate the theoretical results, as well as illustrate the necessity of a proper trajectory.

Torwards uncertainty optimization in active SLAM

This paper addresses the problem of optimizing the uncertainty in an active simultaneous localization and mapping algorithm. This is done by designing an optimization problem that weighs the final uncertainty, the average uncertainty in the horizon considered, and the cost of the control. Using the Pontryagin minimum principle and building on [1] and [2], the optimization problem is transformed into a two-point boundary value problem that encodes necessary conditions for the input that minimizes the uncertainty. The problem is solved numerically, and several particular examples are analysed in depth.

A globally exponentially stable filter for bearing-only simultaneous localization and mapping with monocular vision

Abstract This paper proposes a novel filter for sensor-based bearing-only simultaneous localization and mapping in three dimensions with globally exponentially stable (GES) error dynamics. A nonlinear system is designed, its output transformed, and its dynamics augmented so that the proposed formulation can be considered as linear time-varying for the purpose of observability analysis. This allows the establishment of observability results related to the original nonlinear system that naturally lead to the design of a Kalman filter with GES error dynamics. The performance of the proposed algorithm is assessed resorting to real experiments based on the Rawseeds dataset as well as further realistic simulations.