Geometric mechanics and optimal control problems in multisensor visual tracking

Stimulated by the upsurge in robotics, grids of visual sensors working together are becoming more popular than a single camera gathering mono-sensory visual information. Advantage of having multiple visual sensors is not limited to stereo sensing. The foundations of modelling the mechanical control of multiple cameras is derived from the mechanical models of the human eye plant. There has not been a rigorous treatment on control of visual multisensors in the framework of geometric mechanics. This thesis sheds new light on visual multisensing with a methodical treatment of mechanical control systems.

The mechanical setup of the visual sensor discussed in this study is similar to the Fick Gimbal which has two degrees of freedom known as pan and tilt angles. The mechanical setup is parameterized using the Tait-Brayn parameterization. A Donders’ constraint is used to prevent the torsional rotations which limits the configuration space of a camera to a two dimensional submanifold of SO(3). Next, the coplanarity condition is imposed to couple two sensors in such a way that stereopsis is maintained throughout the gaze shift. Next, the Lagrangian and Hamiltonian descriptions of the composite system are developed. For the Lagrangian, external torques are used instead of generalized torques, and Pontrayagin’s maximum principle is used to find the expression of external torques. Thereafter, this technique is extended to multiple sensors.

Results on multiple dimensions are produced during this study. A method to convert a boundary value problem to an initial value problem is suggested. The expression for the number of coplanarity conditions are formulated. Optimal torques of the sensors close to the Listing’s plane are compared to those away from it. The energy implications on the symmetry of the sensor placement is discussed. Finally, a conjecture is proposed for the multisensor tracking.