Random Finite Sets for Robot Mapping and SLAM
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Machines which perceive the world through the use of sensors, make computational decisions based on the sensors’ outputs and then influence the world with actuators, are broadly labelled as “Robots”. Due to the imperfect nature of all real sensors and actuators, the lack of predictability within real environments and the necessary approximations to achieve computational decisions, robotics is a science which is becoming ever more dependent on probabilistic algorithms. Autonomous robot vehicles are examples of such machines, which are now being used in areas other than the factory floors, and which therefore must operate in unstructured, and possibly previously unexplored environments. Their reliance on probabilistic algorithms, which can interpret sensory data and make decisions in the presence of uncertainty, is increasing. Therefore, mathematical interpretations of the vehicle’s environment which consider all the relevant uncertainty are of a fundamental importance to an autonomous vehicle, and its ability to function reliably within that environment. While a universal mathematical model which considers the vast complexities of the physical world remains an extremely challenging task, stochastic mathematical representations of a robots operating environment are widely adopted by the autonomous robotic community. Probability densities on the chosen map representation are often derived and then recursively propagated in time via the Bayesian framework, using appropriate measurement likelihoods.
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