This paper presents the analytic solution of a fundamental open problem in the framework of state estimation/nonlinear observability, which is the Unknown Input Observability problem (UIO problem). The problem consists in deriving the analytic criterion that allows us to automatically obtain the state observability in presence of disturbances (or unknown inputs). In other words, the problem is to extend the well known observability rank condition to the case when the dynamics are also driven by unknown inputs. Enunciated in the seventies by the control theory community, this problem was only solved in the linear case. The solution here provided holds for nonlinear systems in presence of a single unknown input. The first part of the paper presents this analytic solution. Very surprisingly, the complexity of the overall analytic criterion is comparable to the complexity of the observability rank condition. The second part of the paper applies this analytic criterion to a robotics system when its dynamics are affected by an external disturbance (e.g., due to the presence of wind). To corroborate the results of our observability analysis we perform extensive simulations and we show that, a simple estimator based on an Extended Kalman Filter, provides results that agree with what we could expect from the observability analysis.

This paper presents a theoretical investigation in the framework of visual-inertial sensor fusion and the results here provided are the extension of our previous contribution in [10], [11]. The general goal of this research is to establish minimalistic visual-inertial sensors settings, which still provide full information even in the most challenging situations, i.e., in the case of unknown camera extrinsic calibration, unknown magnitude of the gravity, unknown inertial sensor bias and when only a single point feature is available. The investigation here provided allows us to conclude that, even in the case of a single point feature, the information provided by a sensor suit composed by a monocular camera and two inertial sensors (along two independent axes and where at least one is an accelerometer) is the same as in the case of a complete inertial measurement unit (i.e., when the inertial sensors consist of three orthogonal accelerometers and three orthogonal gyroscopes). To derive this result, an observability analysis of systems with only one and two inertial sensors is performed. This analysis requires to approach an open problem in control theory, called the Unknown Input Observability (UIO). In this paper we adopt the same method introduced in [10], [11] to solve this UIO problem. The method has been here improved in order to deal with systems more complex than the ones analyzed in [10], [11]. The paper also provides a general discussion on UIO and in particular on the proposed solution.

This paper analyzes the observability properties of the visual inertial structure from motion as the number of inertial sensors is reduced. Specifically, instead of considering the standard formulation where the inertial sensors are 3 orthogonal accelerometers and 3 orthogonal gyroscopes, the sensor system here considered only consists of a monocular camera and 1 or 2 accelerometers. This analysis has never been provided before. The main result achieved in this context is that the observability properties of visual inertial structure from motion do not change by removing all the 3 gyroscopes and 1 accelerometer. By removing a further accelerometer, if the camera is not extrinsically calibrated, the system loses part of its observability properties. On the other hand, if the camera is extrinsically calibrated, the system maintains the same observability properties as in the standard case. This contribution clearly shows that the information provided by a monocular camera, 3 accelerometers and 3 gyroscopes is redundant. Additionally, it provides a new perspective in the framework of neuroscience to the process of vestibular and visual integration for depth perception and self motion perception. Finally, to analyze these systems with a reduced number of inertial sensors, the paper introduces a new method to derive the observability properties of a non linear system when part of its input controls is unknown. This method is a further original paper contribution in control theory.

This paper presents a novel method to perform the outlier rejection task between two different views of a camera rigidly attached to an Inertial Measurement Unit (IMU). Only two feature correspondences and gyroscopic data from IMU measurerments are used to compute the motion hypothesis. By exploiting this 2-point motion parametrization, we propose two algorithms to remove wrong data associations in the feature-matching process for case of a 6DoF motion. We show that in the case of a monocular camera mounted on a quadrotor vehicle, motion priors from IMU can be used to discard wrong estimations in the framework of a 2-point-RANSAC based approach. The proposed methods are evaluated on both synthetic and real data.

This paper provides two novel contributions. The former regards the observability of the visual-inertial structure from motion. It is proven that, the information contained in the data provided by a monocular camera which observes a single point-feature and by an Inertial Measurement Unit (IMU) allows estimating the absolute scale, the speed in the local frame, the absolute roll and pitch angles, the biases which affect the accelerometer's and the gyroscope's measurements, the magnitude of the gravitational acceleration and the extrinsic camera-IMU calibration. The latter contribution is the derivation of a new closed form solution to determine some of the previous observable quantities by only using few camera measurements collected during a short time interval and the data provided by the IMU during the same time interval. This closed-solution allows us to investigate the intrinsic properties of the visual-inertial structure from motion and in particular to identify the conditions under which the problem has a finite number of solutions. Specifically, it is shown that the problem can have a unique solution, two distinct solutions and infinite solutions depending on the trajectory, on the number of point-features and on their layout and on the number of camera images. The proposed closed solution is finally used in conjunction with a filter based approach in order to show its benefit.

The objective of this paper is to present a strategy to safely move a robot in an unknown and complex environment where people are moving and interacting. The robot, by using only its sensor data, must navigate respecting humans' comfort. To obtain good results in such a dynamic environment, a prediction on humans' movement is also crucial. To solve all the aforementioned problems we introduce a suitable cost function. Its optimization is obtained by using a new stochastic and adaptive optimization algorithm (CAO). This method is very useful in particular when the analytical expression of the optimization function is unknown but numerical values are available for any state configuration. Additionally, the proposed method can easily incorporate any dynamical and environmental constraints. To validate the performance of the proposed solution, several simulation results are provided.

The SFly project is an EU-funded project, with the goal to create a swarm of autonomous vision controlled micro aerial vehicles. The mission in mind is that a swarm of MAV's autonomously maps out an unknown environment, computes optimal surveillance positions and places the MAV's there and then locates radio beacons in this environment. The scope of the work includes contributions on multiple different levels ranging from theoretical foundations to hardware design and embedded programming. One of the contributions is the development of a new MAV, a hexacopter, equipped with enough processing power for onboard computer vision. A major contribution is the development of monocular visual SLAM that runs in real-time onboard of the MAV. The visual SLAM results are fused with IMU measurements and are used to stabilize and control the MAV. This enables autonomous flight of the MAV, without the need of a data link to a ground station. Within this scope novel analytical solutions for fusing IMU and vision measurements have been derived. In addition to the realtime local SLAM, an offline dense mapping process has been developed. For this the MAV's are equipped with a payload of a stereo camera system. The dense environment map is used to compute optimal surveillance positions for a swarm of MAV's. For this an optimiziation technique based on cognitive adaptive optimization has been developed. Finally, the MAV's have been equipped with radio transceivers and a method has been developed to locate radio beacons in the observed environment.

In this paper we consider an aerial vehicle equipped with a monocular camera and inertial sensors. Additionally, a laser pointer is mounted on the vehicle and it produces a laser spot. The laser spot is observed by the monocular camera and it is the unique point feature used in the proposed approach. We focus our attention to the case when the vehicle moves in proximity of a planar surface and in particular when the laser spot belongs to this surface. The paper provides two main contributions. The former is the analytical derivation of all the observable modes, i.e. all the physical quantities that can be determined by only using the inertial data and the camera observations of the laser spot during a short time-interval. Specifically, it is shown that the observable modes are: the distance of the vehicle from the planar surface; the component of the vehicle speed, which is orthogonal to the planar surface; the relative orientation of the vehicle with respect to the planar surface; the orientation of the planar surface with respect to the gravity. The second contribution is the introduction of a simple recursive method to perform the estimation of all the aforementioned observable modes. This method is based on a local decomposition of the original system, which separates the observable modes from the rest of the system. The method is validated by using synthetic data. Additionally, preliminary tests with real data are provided and more complete experiments are in progress. The presented approach can be integrated in the framework of autonomous take-off and landing, safe touch-down and low altitude manoeuvres even in dark or featureless environment.

This paper investigates the problem of vision and inertial data fusion. A sensor assembling that is constituted by one monocular camera, three orthogonal accelerometers, and three orthogonal gyroscopes is considered. The first paper contribution is the analytical derivation of all the observable modes, i.e., all the physical quantities that can be determined by only using the information in the sensor data that are acquired during a short time interval. Specifically, the observable modes are the speed and attitude (roll and pitch angles), the absolute scale, and the biases that affect the inertial measurements. This holds even in the case when the camera only observes a single point feature. The analytical derivation of the aforementioned observable modes is based on a nonstandard observability analysis, which fully accounts for the system nonlinearities. The second contribution is the analytical derivation of closed-form solutions, which analytically express all the aforementioned observable modes in terms of the visual and inertial measurements that are collected during a very short time interval. This allows the introduction of a very simple and powerful new method that is able to simultaneously estimate all the observable modes with no need for any initialization or a priori knowledge. Both the observability analysis and the derivation of the closed-form solutions are carried out in several different contexts, including the case of biased and unbiased inertial measurements, the case of a single and multiple features, and in the presence and absence of gravity. In addition, in all these contexts, the minimum number of camera images that are necessary for the observability is derived. The performance of the proposed approach is evaluated via extensive Monte Carlo simulations and real experiments.

This paper presents a closed-form solution for metric velocity estimation of a single camera using inertial measurements. It combines accelerometer and attitude measurements with feature observations in order to compute both the distance to the feature and the speed of the camera inside the camera frame. Notably, we show that this is possible by just using three consecutive camera positions and a single feature correspondence. Our approach represents a compact linear and multirate solution for estimating complementary information to regular essential matrix computation, namely the scale of the problem. The algorithm is thoroughly validated on simulated and real data and conditions for good quality of the results are identified.

This paper considers the problem of data fusion when the adopted sensors are a monocular camera and inertial sensors (i.e. one tri-axial accelerometer and one tri-axial gyrometer). The investigation starts by performing an observability analysis to analytically derive all the observable modes, i.e. all the physical quantities that the information contained in the sensor data allows us to estimate. They are the position of the features in the camera frame, the vehicle speed in the same local frame and the absolute roll and pitch angles. The main contribution of the paper is a new algorithm to simultaneously estimate all the previous physical quantities. In particular, the algorithm is based on a closed-form solution which analytically expresses the vehicle speed and attitude in terms of the sensor measurements. In this algorithm the camera only needs to observe four times a single point feature in the environment. This allows performing the overall estimation in a very short time interval and without the need of any initialization or a priori knowledge. This is a key advantage since allows eliminating the drift on the scale factor and on the vehicle orientation. In addition, the algorithm can be easily extended in order to deal with biased inertial measurements and to deal with multiple features, in which case only three distinct camera poses are required (instead of four). Specifically, with three camera poses and two features, the vehicle speed and attitude together with the scale factor can be determined. The performance of the proposed approach is evaluated via Monte Carlo simulations and by using real data.

This paper investigates the problem of determining the speed and the attitude of a vehicle equipped with a monocular camera and inertial sensors. The vehicle moves in a 3D unknown environment. It is shown that, by collecting the visual and inertial measurements during a very short time interval, it is possible to determine the following physical quantities: the vehicle speed and attitude, the absolute distance of the point features observed by the camera during the considered time interval and the bias affecting the inertial measurements. In particular, this determination, is based on a closed form solution which analytically expresses the previous physical quantities in terms of the sensor measurements. This closed form determination allows performing the overall estimation in a very short time interval and without the need of any initialization or prior knowledge. This is a key advantage since allows eliminating the drift on the absolute scale and on the vehicle orientation. In addition, the paper provides the minimum number of distinct camera images which are needed to perform this determination. Specifically, if the magnitude of the gravity is unknown, at least four camera images are necessary while if it is a priori known, three camera images are necessary. The performance of the proposed approach is evaluated by using real data.

This paper considers the problem of state estimation in autonomous navigation from a theoretical perspective. In particular, the investigation concerns problems where the information provided by the sensor data is not sufficient to carry out the state estimation (i.e., the state is not observable). For these systems, the concept of continuous symmetry is introduced. Detection of the continuous symmetries of a given system has a very practical importance. It allows the detection of an observable state whose components are nonlinear functions of the original nonobservable state. So far, this theoretical and very general concept has been applied to deal with two distinct fundamental estimation problems in the framework of mobile robotics. The former is in the framework of self-calibration, and the latter is in the framework of the fusion of the data provided by inertial sensors and vision sensors. For reasons of length, only the former is discussed. In particular, the theoretical machinery is used to address a specific calibration problem. The solution constrains the robot to move along specific trajectories in order to be able to apply the calibration algorithm. This paper provides two distinct contributions. The first is the introduction of this concept of continuous symmetry. The second is the introduction of a simple and efficient strategy to extrinsically calibrate a bearing sensor (e.g., a vision sensor) mounted on a vehicle and, simultaneously, estimate the parameters describing the systematic error of its odometry system. Many accurate simulations and real experiments show the robustness, the efficiency, and the accuracy of the proposed strategy.

In this paper, the problem of positioning a team of mobile robots for a surveillance task in a non-convex environment with obstacles is considered. The robots are equipped with global positioning capabilities (for instance they are equipped with GPS) and visual sensors able to monitor the surrounding environment. Furthermore, they are able to communicate one with each other. The goal is to maximize the area monitored by the team, by identifying the best configuration of the team members. Due to the non-convex nature of the problem, an analytical solution can not be obtained. The proposed method is based on a new cognitive-based, adaptive optimization algorithm (CAO). This method allows getting coordinated and scalable controls to accomplish the task, even when the obstacles are unknown and the team is heterogeneous, i.e. each robot is equipped with a different type of visual sensor. Extensive simulations are presented to show the efficiency of the proposed approach.

This paper considers the problem of sensor self-calibration in mobile robotics by only using a single point feature (e.g. a source of light). In particular, the problem of determining the extrinsic parameters of a bearing sensor mounted on a mobile platform (e.g. a camera) and simultaneously estimating the parameters describing the systematic error in the odometry system is discussed. Special attention is devoted to investigate the dependence of the observability properties of these parameters on the chosen robot trajectory. The main contribution provided by this paper is the introduction of a new method to deal with estimation problems in the framework of mobile robotics. Specifically, a calibration problem has been considered. However, the same method can be adopted to solve other fundamental estimation problems. The method is based on the theory of distributions which exploits all the system Lie symmetries. Regarding the considered calibration problem this method allows analytically detecting the combinations of the calibration parameters which are observable for a given robot trajectory. Experiments are provided to validate the results.

This paper presents a distributed Maximum A Posteriori (MAP) estimator for multi-robot Cooperative Localization (CL). As opposed to centralized MAP-based CL, the proposed algorithm reduces the memory and processing requirements by distributing data and computations amongst the robots. Specifically, a distributed data-allocation scheme is presented that enables robots to simultaneously process and update their local data. Additionally, a distributed Conjugate Gradient algorithm is employed that reduces the cost of computing the MAP estimates, while utilizing all available resources in the team and increasing robustness to single-point failures. Finally, a computationally efficient distributed marginalization of past robot poses is introduced for limiting the size of the optimization problem. The communication and computational complexity of the proposed algorithm is described in detail, while extensive simulation studies are presented for validating the performance of the distributed MAP estimator and comparing its accuracy to that of existing approaches.

This paper introduces a new analytical algorithm to perform the localization of a mobile robot using odometry and laser readings. Based on a polynomial approach, the proposed algorithm provides the optimal affine filter in a class of suitably defined estimators. The performance of the algorithm has been evaluated through simulations. The comparison with the standard Extended Kalman Filter shows that the proposed filter provides good estimates also in critical situations where the system nonlinearities cause a bad behavior of the EKF.

This paper presents two methods able to exploit the information at the loop closure in the SLAM problem. Both methods have three fundamental advantages. The first one is that to apply the loop closure constraint they do not require to compute any correlation among the features which are not observed simultaneously. The second advantage is that the loop closure constraint can be applied only once at the end (even after more than one loop) in a single step with low computational complexity. Hence, the computational complexity during the robot exploration is independent of the number of features. Finally, the third advantage is that the linearization does not affect the estimation process. This especially holds for the second method, which is based on the Levenberg-Marquardt algorithm. The first method is based on the extended Kalman filter. Simulations show that these approaches significantly outperform the conventional EKF based SLAM both in the computational cost and in the map precision.

This paper introduces a new approach to the problem of simultaneously localizing a team of mobile robots equipped with proprioceptive sensors able to monitor their motion and with exteroceptive sensors able of sensing one another. The method is based on a series of extended Kalman filters hierarchically distributed. In particular, the team is decomposed in several groups and, for each group, an extended Kalman filter estimates the configurations of all the members of the group in a local frame attached to one robot, the group leader. Finally, at the highest level of the hierarchy, one single filter estimates the locations of all the group leaders. The key advantage of this approach is its ability to distribute the computation necessary to perform the multi robot localization under limited computation and communication capabilities. In particular, the approach significantly outperforms an optimal approach based on a single estimator. This is shown by analytically computing the precision on the localization of each robot in the case of one single degree of freedom. In particular, the best hierarchy is analytically determined by deriving the dependency of the localization precision on the communication and computation capabilities and on the sensors accuracy.

This paper presents a new technique to estimate the extrinsic parameters of a robot-vision sensor system. More in general, this technique can be adopted to calibrate any robot bearing sensor. It is based on the extended Kalman filter. It is very simple and allows an automatic self-calibration during the robot motion. It only requires a source of light in the environment and an odometry system on the robot. The strategy is theoretically validated through an observability analysis which takes into account the system nonlinearities. This analysis shows that the system contains all the necessary information to perform the self-calibration. Furthermore, many accurate simulations and experiments performed on a real platform equipped with encoder sensors and an omnidirectional conic vision sensor, show the exceptional performance of the strategy

In this paper, we present a flexible new technique for single viewpoint omnidirectional camera calibration. The proposed method only requires the camera to observe a planar pattern shown at a few different orientations. Either the camera or the planar pattern can be freely moved. No a priori knowledge of the motion is required, nor a specific model of the omnidirectional sensor. The only assumption is that the image projection function can be described by a Taylor series expansion whose coefficients are estimated by solving a two-step least-squares linear minimization problem. To test the proposed technique, we calibrated a panoramic camera having a field of view greater than 200 in the vertical direction, and we obtained very good results. To investigate the accuracy of the calibration, we also used the estimated omni-camera model in a structure from motion experiment. We obtained a 3D metric reconstruction of a scene from two highly distorted omnidirectional images by using image correspondences only. Compared with classical techniques, which rely on a specific parametric model of the omnidirectional camera, the proposed procedure is independent of the sensor, easy to use, and flexible.

In this paper we derive theoretical results for the problem of on-line sensor calibration for a mobile robot. We consider the case of the odometry sensor. A first series of results regards the problem of understanding if a given system (consisting of a robot with several sensors) contains the necessary information to perform the on-line self calibration of one of its sensors. We consider several cases corresponding to different odometry systems and different types of robot sensors. Finally, we also consider the problem of maximizing the calibration accuracy and we formulate this problem as an optimal control problem. For the special case of a holonomic vehicle, we derive an analytical solution, i.e. we find the best trajectory which maximizes the calibration accuracy

Today, lightweight SLAM algorithms are needed in many embedded robotic systems. In this paper the orthogonal SLAM (OrthoSLAM ) algorithm is presented and empirically validated. The algorithm has constant time complexity in the state estimation and is capable to run real-time. The main contribution resides in the idea of reducing the complexity by means of an assumption on the environment. This is done by mapping only lines that are parallel or perpendicular to each other which represent the main structure of most indoor environments. The combination of this assumption with a Kalman filter and a relative map approach is able to map our laboratory hallway with the size of 80 m times 50 m and a trajectory of more than 500 m. The precision of the resulting map is similar to the measurements done by hand which are used as the ground-truth

In this paper, the independence relative map algorithm is presented. The algorithm aims to achieve the independence of relative map states. We show that using dependent relative quantities from the same observation creates a bias to the state covariance matrix, leading to an inaccurate and inconsistent relative map. Having independent map states improves the map consistency. Two case studies are presented in which we apply the proposed algorithm together with two popular relative map methods. Experimental results on simulated data show that the integrated algorithms outperform the original methods in term of map consistency and algorithm speed

In this paper, we present a novel technique for calibrating central omnidirectional cameras. The proposed procedure is very fast and completely automatic, as the user is only asked to collect a few images of a checker board, and click on its corner points. In contrast with previous approaches, this technique does not use any specific model of the omnidirectional sensor. It only assumes that the imaging function can be described by a Taylor series expansion whose coefficients are estimated by solving a four-step least-squares linear minimization problem, followed by a non-linear refinement based on the maximum likelihood criterion. To validate the proposed technique, and evaluate its performance, we apply the calibration on both simulated and real data. Moreover, we show the calibration accuracy by projecting the color information of a calibrated camera on real 3D points extracted by a 3D sick laser range finder. Finally, we provide a Toolbox which implements the proposed calibration procedure

In this paper we consider the problem of simultaneously localizing all members of a team of robots. Each robot is equipped with proprioceptive sensors and exteroceptive sensors. The latter provide relative observations between the robots. Proprioceptive and exteroceptive data are fused with an Extended Kalman Filter. We derive the equations for this estimator for the most general relative observation between two robots. Then we consider three special cases of relative observations and we present the structure of the filter for each case. Finally, we study the performance of the approach through many accurate simulations.

In [5], a version of Relative Map Filter (RMF) is proposed to solve the simultaneous localization and map building (SLAM) problem. In the RMF, the map states contain only quantities invariant under shift and rotation. The estimation of the map states and their correlations is carried out in an optimal way using the Kalman filter. However, the dependency among the map states is not taken into account, thus the resulting map states are inconsistent. This paper presents two methods to enforce the consistency of the relative map states. The idea is to maintain a geometrically consistent map by solving a set of constraints between the map states. Experimental results obtained by using the proposed methods on real platform data show better performance than those deduced from the original RMF.

In this paper, the problem of localize two mobile robots is considered. The robots are equipped with proprioceptive sensors (like encoders) and exteroceptive sensors able to provide relative observations between them. In these observations, one robot detects and identifies the other one and measures some relative quantity. An observability analysis is performed by taking into account the system nonlinearities and for four different relative observations. The theoretical results are validated by simulations and experiments carried out on real platforms. In these experiments, an extended Kalman filter is adopted to fuse the information coming from the encoders and the sensors performing the observations.

This paper addresses the closing loop problem as the challenge of using all the information from the observation gathered when closing the loop in order to optimally adjust the whole map (assuming a correct data association). The proposed approach is an approximation, which allows the calculation of the gain without keeping track of all the correlations (i.e. with a complexity independent of the number of the map elements). Furthermore, the paper presents an explicit mathematical demonstration showing that the correlations computed by the EKF-based SLAM are overestimated. More precisely, it is shown that these correlations decrease exponentially with respect to the heading error of the robot. The approach is empirically demonstrated by means of meaningful simulations. The results are then discussed and conclusions are pointed out in the last section.

This paper presents an experimental evaluation of different line extraction algorithms on 2D laser scans for indoor environment. Six popular algorithms in mobile robotics and computer vision are selected and tested. Experiments are performed on 100 real data scans collected in an office environment with a map size of 80m /spl times/ 50m. Several comparison criteria are proposed and discussed to highlight the advantages and drawbacks of each algorithm, including speed, complexity, correctness and precision. The results of the algorithms are compared with the ground truth using standard statistical methods.

This paper starts with a discussion of the open challenges in the SLAM problem. In our opinion they can be grouped in two main and distinct areas: convergence of the built map and computation requirement for real world application. To deal with the previous problems, a solution in the stochastic map framework based on the concept of the relative map is proposed. The idea consists in introducing a map state, which only contains quantities invariant under shift and rotation and to carry out the estimation of this relative map in an optimal way. This is a possible way in order to have a decoupling between the robot motion and the landmark estimation and therefore not to rely the landmark estimation on the unmodeled error sources of the robot motion. Moreover, the proposed solution scales linearly with the number of landmark allowing real-time application. Experimental results, carried out on a real platform, show the better performance of this method with respect to the joint vehicle-landmark approach (absolute map filter) when the odometry is affected by undetected systematic errors or by large or unmodeled non-systematic errors.

This paper presents a solution to the simultaneous localization and mapping (SLAM) problem in the stochastic map framework for a mobile robot navigating in an indoor environment. The approach is based on the concept of the relative map. The idea consists in introducing a map state, which only contains quantities invariant under translation and rotation. This is done in order to have a decoupling between the robot motion and the landmark estimation and therefore not to rely the landmark estimation on the unmodeled error sources of the robot motion. The case of the corner feature is here considered. The relative state estimated through the Kalman filter contains the distances and the relative orientations among the corners observed at the same tune. Therefore, this state is invariant with respect to the robot configuration (translation and rotation). Finally, an environment containing structures consisting of several corners is also investigated. Real experiments carried out with a mobile robot equipped with a 360/spl deg/ laser range finder show the performance of the approach.

This paper presents both the theory and the first experimental results of a new method which allows simultaneous estimation of the robot configuration and the odometry error (both systematic and non-systematic) during the mobile robot navigation. The estimation of the non-systematic components is carried out through an augmented Kalman filter which estimates a state containing the robot configuration and the parameters of the odometry error. It uses encoder readings as inputs and the readings from a laser range finder as observations. The estimation of the non-systematic components is carried out through another Kalman filter where the observations are obtained by two subsequent robot configurations provided by the previous augmented Kalman filter.

In this paper the odometry error of a mobile robot with a synchronous drive system is modeled by introducing four parameters characterizing its systematic and non-systematic components (translational and rotational). A strategy in order to simultaneously estimate the model parameters is suggested. This strategy only requires to measure the change in the orientation and in the position between the initial and the final configuration of the robot related to suitable robot motions. In other words, it is unnecessary to know the actual path followed by the robot. The proposed strategy is illustrated by discussing the accuracy on the parameter estimation both in an indoor and outdoor environment.

This paper focuses on issues of odometry for the special case of synchronous drive wheeled mobile robots. In particular, the uncertainty in odometry is modeled by a four parameter statistical model already introduced in previous works together with a strategy to estimate the four parameters from actual data obtained from a given mobile robot. To obtain the data, the robot traverses a path. The error realized along that path is then used to estimate the model parameters. The accuracy on the parameter estimation through this strategy is here discussed by considering paths different for length and shape.

This paper presents an error modeling of an odometry system for a synchronous-drive system and a possible strategy for evaluating this error. The odometry error is modeled by introducing four parameters characterizing its systematic and nonsystematic components (translational and rotational). The nonsystematic errors are expressed in terms of a covariance matrix, which depends on both the previous four parameters and the path followed by the mobile robot. In contrast to previous approaches which require assuming a particular path (straight or circular) in order to compute this covariance matrix, the general formulas are derived. We suggest a possible strategy for simultaneously estimating the four model parameters. It is shown that our strategy only requires measuring the change in the orientation and position between the initial and final configurations of the robot, related to suitable robot motions. In other words, it is unnecessary to know the actual path followed by the robot. We illustrate the proposed strategy by discussing the accuracy of the parameters estimation, and present some of the experimental results obtained with the mobile robot Nomad 150.

The odometry error of a mobile robot contains both systematic and non-systematic components. This paper presents an error modeling of an odometry system for a synchronous drive system and a possible strategy in order to evaluate this error. The odometry error is modeled by introducing four parameters characterizing its systematic and non-systematic components (translational and rotational). We introduce five experimentally measurable quantities for a given robot motion, which we call observables. On the basis of our odometry error model we analytically compute the average values of the observables, which depend on the previous four parameters and on the considered robot motion. We suggest a possible strategy in order to simultaneously estimate the four parameters by estimating the observables. We show that our strategy only requires to measure the change in the orientation and position between the initial and the final configuration of the robot related to suitable robot motions. The strategy was applied to the platform Nomad150.