Abstract—The simultaneous localization and map building (SLAM) problem asks if it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and then to incrementally build a map of this environment while simultaneously using this map to compute absolute vehicle location. Starting from the estimation-theoretic foundations of this problem developed in [1]–[3], this paper proves that a solution to the SLAM problem is indeed possible. The underlying structure of the SLAM problem is first elucidated. A proof that the estimated map converges monotonically to a relative map with zero uncertainty is then developed. It is then shown that the absolute accuracy of the map and the vehicle location reach a lower bound defined only by the initial vehicle uncertainty. Together, these results show that it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and, using relative observations only, incrementally build a perfect map of the world and to compute simultaneously a bounded estimate of vehicle location. This paper also describes a substantial implementation of the SLAM algorithm on a vehicle operating in an outdoor environment using millimeter-wave (MMW) radar to provide relative map observations. This implementation is used to demonstrate how some key issues such as map management and data association can be handled in a practical environment. The results obtained are cross-compared with absolute locations of the map landmarks obtained by surveying. In conclusion, this paper discusses a number of key issues raised by the solution to the SLAM problem including suboptimal map-building algorithms and map management. Index Terms—Autonomous navigation, millimeter wave radar, simultaneous localization and map building. I.

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Abstract — This paper studies the time evolution of the covariance of the position estimates in single-robot Simultaneous Localization And Mapping (SLAM). A closed-form expression is derived, that establishes a functional relation between the noise parameters of the robot’s proprioceptive and exteroceptive sensors, the number of features being mapped, and the attainable accuracy of SLAM. Furthermore, it is demonstrated how prior information about the spatial density of landmarks can be utilized in order to compute a tight upper bound on the expected covariance of the positioning errors. The derived closed-form expressions enable the prediction of SLAM positioning performance, without resorting to extensive simulations, and thus offer an analytical tool for determining the sensor characteristics required to achieve a desired degree of accuracy. Simulation experiments are conducted, that corroborate the presented theoretical analysis. I.

The solution to the simultaneous localization and map building (SLAM) problem where an autonomous vehicle starts in an unknown location in an unknown environment and then incrementally build a map of landmarks present in this environment while simultaneously using this map to compute absolute vehicle location is now well understood. Although a number of SLAM implementations have appeared in the recent literature, the need to maintain the knowledge of the relative relationships between all the landmark location estimates contained in the map makes SLAM computationally intractable in implementations containing more than a few tens of landmarks. This paper presents the theoretical basis and a practical implementation of a feature selection strategy that significantly reduces the computation requirements for SLAM. The paper shows that it is indeed possible to remove a large percentage of the landmarks from the map without making the map building process statistically inconsistent. Furthermore, it is shown that the computational cost of the SLAM algorithm can be reduced by judicious selection of landmarks to be preserved in the map.

In this report we derive analytical upper bounds on the covariance of the state estimates in SLAM. The analysis is based on a novel formulation of the SLAM problem, that enables the simultaneous estimation of the landmark coordinates with respect to the a robot-centered frame (relative map), as well as with respect to a fixed global frame (absolute map). A study of the properties of the covariance matrix in this formulation yields analytical upper bounds for the uncertainty of both map representations. Moreover, by employing results from Least Squares estimation theory, the guaranteed accuracy of the robot pose estimates is derived as a function of the accuracy of the robot’s sensors, and of the properties of the map. Contrary to previous approaches, the method presented here makes no assumptions about the availability of a sensor measuring the absolute orientation of the robot. The theoretical analysis is validated by simulation results and real-world experiments. 1

This paper describes a Sliding Window Filter (SWF) that is a constant-time approximation to the feature-based batch non-linear least squares Simultaneous Localization and Mapping (SLAM) problem. In particular, we are interested in improving the range resolution of stereo vision for Entry, Descent and Landing (EDL) missions to Mars and other planetary bodies. The goal is to create accurate and precise 3D planetary surface structure estimates by filtering sequences of stereo images taken from an autonomous landing vehicle. More generally we are interested in fast, optimal, relative spatial estimation for mobile robots. The SWF is useful in this context because it can scale from the offline, optimal batch least squares solution to fast online incremental solutions. For instance, if the window encompasses all time, the solution is algebraically equivalent to full SLAM; if only one time step is maintained, the solution is algebraically equivalent to the Extended Kalman Filter SLAM solution; if robot poses and environment landmarks are slowly marginalized out over time such that the state vector ceases to grow, then the filter becomes constant time, like Visual Odometry. Further, the sliding window method exhibits other interesting properties, like reversible data association, out-of sequence measurement updates, and robust estimation across multiple timesteps. We test the SWF with image data captured to emulate EDL conditions for a Mars lander. Experiments show that structure estimates derived from the SWF converge to the optimal result predicted by theory. To the best of our knowledge, this is the first work to show optimal

I hereby declare that this submission is my own work and that, to the best of my knowledge and belief, it contains no material previously published or written by another person nor material which to a substantial extent has been accepted for the award of any other degree or diploma of the University or other institute of higher learning, except where due acknowledgement has been made in the text.

The simultaneous localization and mapping (SLAM) problem has been investigated by many researchers, and solutions frequently rely on sensor based approaches, such as very accurate range/bearing sensors (mmw radar, laser rangefinders, imaging sonar) which measure the position of landmarks in the environment relative to the robot and complex kinematic vehicle models or inertial naviation systems which measure the motion of the robot through the environment. Some solutions also require that the robot can measure orientation by some accurate and external means, reducing pose estimation to position estimation. These solutions tend to rely on a Kalman Filter or Extended Kalman Filter to recursively estimate both the map and robot pose in one global, absolute coordinate system. In the proposed research, I will address the SLAM problem for an autonomous mobile robot in an unstructured environment using landmark bearing measurements and dead reckoning as its only means of sensing. I will investigate the use of a representation of the environment which parameterizes relationships between landmarks rather than their position in a global, absolute coordinate frame. These relationships are invariant to the position from which landmarks are observed, decoupling the uncertainties in landmark positions and robot position. This decoupling has implications on the way in which sensor fusion is done and the uncertainty in the environment map and robot position estimates which result. The aim of this research is to provide a more general framework for SLAM applicable over a wider range of scenarios, and to provide a solution to the SLAM problem that is efficient, scalable, and robust to sensing and modeling errors.

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