Certainty grids, a numerical representation of uncertain and incomplete sensor data, have been successfully used in mobile robot control programs. They offer a powerful and efficient solution for sensor fusion, motion planning, landmark identification, and other central problems. Early success was achieved with ad-hoc formulas for updating grid cells, but a new Bayesian statistical foundation promises further improvements. A software framework is proposed for the Uranus mobile robot to maintain a probabilistic, geometric map of its surroundings as it moves. The certainty grid representation allows the map to be incrementally updated from various sources, including sonar, stereo vision, proximity, and contact sensors. The approach can model the fuzziness of each reading, combine multiple measurements to produce sharper map features, and correctly handle uncertainties in the robot's motion. The map will be used for path planning, location identification, terrain identification, and object identification by shape. The certainty grid can also be extended in time to detect and track moving objects. Even simple versions of the idea allow the robot to perform tasks previously out of reach. The robot can explore a region and return to its starting point using map snapshots from its outbound journey, even in the presence of motion disturbances and terrain changes. Robot motion planning systems have traditionally used hard-edged models, with positional uncertainty expressed as a Gaussian spread. However, incomplete error modeling can reduce positional accuracy and lead to faulty conclusions. Programs that neglect uncertainties and alternative interpretations are brittle, as small errors can be amplified, leading to incorrect actions. Numerical representations, such as those used in the Stanford Cart, have shown promise in escaping this fate. In the Stanford Cart, stereo depth measurements from 36 pairings of nine images were combined in a 1000-cell array, with the largest peak giving the correct range. This procedure was the most error-tolerant step in the Cart navigator, but alone it did not protect the whole program from brittleness.Certainty grids, a numerical representation of uncertain and incomplete sensor data, have been successfully used in mobile robot control programs. They offer a powerful and efficient solution for sensor fusion, motion planning, landmark identification, and other central problems. Early success was achieved with ad-hoc formulas for updating grid cells, but a new Bayesian statistical foundation promises further improvements. A software framework is proposed for the Uranus mobile robot to maintain a probabilistic, geometric map of its surroundings as it moves. The certainty grid representation allows the map to be incrementally updated from various sources, including sonar, stereo vision, proximity, and contact sensors. The approach can model the fuzziness of each reading, combine multiple measurements to produce sharper map features, and correctly handle uncertainties in the robot's motion. The map will be used for path planning, location identification, terrain identification, and object identification by shape. The certainty grid can also be extended in time to detect and track moving objects. Even simple versions of the idea allow the robot to perform tasks previously out of reach. The robot can explore a region and return to its starting point using map snapshots from its outbound journey, even in the presence of motion disturbances and terrain changes. Robot motion planning systems have traditionally used hard-edged models, with positional uncertainty expressed as a Gaussian spread. However, incomplete error modeling can reduce positional accuracy and lead to faulty conclusions. Programs that neglect uncertainties and alternative interpretations are brittle, as small errors can be amplified, leading to incorrect actions. Numerical representations, such as those used in the Stanford Cart, have shown promise in escaping this fate. In the Stanford Cart, stereo depth measurements from 36 pairings of nine images were combined in a 1000-cell array, with the largest peak giving the correct range. This procedure was the most error-tolerant step in the Cart navigator, but alone it did not protect the whole program from brittleness.