We are developing a mobile robot capable of emulating general 6-degree-of-freedom spacecraft relative motion. The omni-directional base uses a trio of active split offset castor drive modules to provide smooth, holonomic, precise control of its motion. Encoders measure the rotations of the six wheels and the three castor pivots. We present a generic odometric algorithm using a least squares framework which is applicable to vehicles with two or more castors and apply it to our unique vehicle configuration. As the accuracy of odometry algorithms depends on the accuracy to which the model parameters are known, a method to perform calibration on the physical robot is needed. We present a geometric calibration method based solely on internal sensor measurements. We present a range of simulation results comparing our odometry results to other algorithms under various systematic and non-systematic errors. We evaluate the ability of our calibration method to accurately determine the true values of our system parameters. The odometry algorithm was also implemented and tested in hardware on our robotic platform. The results presented in the paper validate the calibration and odometry algorithms in both simulation and hardware.

Direction-dependent scaling, shaping, and rotation of Gaussian basis functions are introduced for maximal trend sensing with minimal parameter representations for input output approximation. It is shown that shaping and rotation of the radial basis functions helps in reducing the total number of function units required to approximate any given input-output data, while improving accuracy. Several alternate formulations that enforce minimal parameterization of the most general radial basis functions are presented. A novel "directed graph" based algorithm is introduced to facilitate intelligent direction based learning and adaptation of the parameters appearing in the radial basis function network. Further, a parameter estimation algorithm is incorporated to establish starting estimates for the model parameters using multiple windows of the input-output data. The efficacy of direction-dependent shaping and rotation in function approximation is evaluated by modifying the minimal resource allocating network and considering different test examples. The examples are drawn from recent literature to benchmark the new algorithm versus existing methods.