Mathematical Foundations of Navigation and Perception for an Autonomous Mobile Robot

This paper concerns the application of techniques from estimation theory to the problem of navigation and perception for a mobile robot. After a brief introduction, a hierarchical architecture is presented for the design of a mobile robot navigation system. The control system for a mobile robot is found to decompose naturally into a hierarchy of control loops, where the levels are defined by the abstraction of the data and the cycle time of the feed-back control. The levels that occur naturally are identified as the level of signal, device, behaviour, and task. Estimation of the position of the vehicle with respect to the external world is fundamental to navigation. Modeling the contents of the immediate environment is equally fundamental. Estimation theory is provides a basic set of tools for position estimation and environmental modeling. These tools provide an elegant and formally sound method for combining internal and external sensor information from different sources, operating at different rates. The foundations of estimation theory are reviewed, and mathematical tools are derived for combining sensory information. In particular, a predict-match-update cycle is derived as a framework for perception. The Kalman filter is shown to provide the mathematical basis for this process. Robot arms require an "arm controller" to command joint motors to achieve a coordinated motion in an external Cartesian coordinate space. In the same sense, robot vehicles require a "vehicle controller" to command the motors to achieve a coordinated motion specified in terms of an external Cartesian coordinate space. The fourth section describes the design of a general purpose vehicle controller based on a Kalman filter. The vehicle controller is designed as a three layer structure. The top layer is an interpreter which assures a control protocol based on asynchronous commands and independent control of orientation and forward displacement. The middle layer is a control loop which maintains an estimate of the vehicle's position and orientation, as well as their uncertainties. The control loop generates estimates and commands translation and rotation in terms of a "virtual vehicle". The bottom layer is a translator between the "virtual vehicle" and whatever physical vehicle on which the controller is implemented. The use of a Kalman filter as the basis for a vehicle controller makes it possible to correct errors in odometric position estimation using external perception. In the fifth section, example cases are derived for correcting a position estimate from different forms of perception. In particular, techniques are presented for correction of estimated position using angle and distance to a landmark, using the angle to a landmark, and using the distance to a landmark.