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Discrete Configuration Space Methods for Determining Modular Connector Area of Acceptance in Higher Dimensions

Physical connectors with self-aligning geometry aid in the docking process for many robotic and automatic control systems such as robotic self-reconfiguration and air-to-air refueling. This self-aligning geometry provides a wider range of acceptable error tolerance in relative pose between the two rigid objects, increasing successful docking chances. We present a new method for computing the error range (or area of acceptance) for a pair of rigid connector objects with self-aligning geometry capable of higher dimensional analysis which was previously limited to three. The method is based on the configuration space obstacle model, which gives us a representation of the space of contact states between the two objects. Using an approach direction as analogous to gravity, and assuming the target docked configuration is stable, the set of misaligned points that lead to docking is the target configuration's watershed for an arbitrarily dimensioned configuration space obstacle. It is well known that the watershed of a height map on a discrete grid can be found using any number of algorithms from image segmentation. We present an implementation based on Meyer's flooding algorithm to determine this watershed and measure the AA for simple connectors in 2D and 3D. Results are presented for systems including unconstrained motion in SE(2) and motion constrained to four dimensions (ie. x,y,z,pitch) in SE(3).