Developing convex methods for robust trajectory planning and feedback gain synthesis for linear systems with state- and control-dependent perturbations.
Summary
This work considers the problem of simultaneous open-loop trajectory design and feedback gain co-design to develop an algorithm for robustly-constrained trajectory optimization for linear time-varying systems with state- and control-dependent perturbations. This extends our previous work to handle optimization of feedback gains to minimize the effect of external perturbations. This could have applications in e.g. vehicle design, by allowing trajectory optimization techniques to be fed back into the vehicle design phase, informing guidance, navigation, and control system requirements. My method relies on the theory of convex duality to convert robust linear inequality constraints into exactly-equivalent deterministic convex constraints, resulting in a computationally-tractable zero-conservatism method for trajectory optimization. The development of the feedback gain optimization algorithm is our latest contribution, allowing the further optimization of a system's nominal trajectory beyond what our previous open-loop methods could accomplish.