Incentivizing Local Controllability in Optimal Trajectory Planning.

Controllability metrics are used to determine or incentivise the ease with which a system can be driven to a specified target. Such metrics stemming from the controllability gramian are currently used to analyse the local controllability of nonlinear systems about precomputed trajectories. This paper introduces an alternative application of these metrics to generate an optimal trajectory that directly incentivises the local controllability of a nonlinear system. Such optimal trajectory design techniques would be useful for reducing the additional control energy requirement necessary to achieve control objective satisfaction in the presence of unmodelled disturbances. We present an approach in which the LTV controllability gramian is used to construct an augmented optimal control problem that incentivises the local controllability of a nonlinear system about the optimal trajectory. A modified form of Zermelo's boat problem is used to demonstrate the approach, showing that trajectories generated by solution of the augmented optimal control problem require the system to expend less additional control energy to recover the optimal terminal state following perturbation due to an unmodelled disturbance.