This work develops an active feedback control law that provides robust regulation for a pendulating platform attached to a new class of land vehicle. The biplanar bicycle is a novel two-wheeled single-axle differentially driven vehicle. The vehicle generates locomotive torques by driving against a reaction mass (comprised of the main chassis, motors, etc.), which is free to rotate. The lack of a fixed-orientation mount for peripheral and excitation-sensitive equipment may be a major disadvantage of this new vehicle class. However, active feedback control using a second reaction or proof mass to stabilize a platform fills this need. Here, the procedure for modeling and control of such a structure is demonstrated through the example of a camera spar for an autonomous biplanar bicycle. The dynamics of the example are developed using Lagrangian techniques. The application of optimal control theory to a linearized approximation of the plant is shown to provide robust regulation, with respect to perturbations and external disturbances, of the fully nonlinear system.