Robots are never perfectly certain about their position or state, so motion planners must account for this uncertainty to ensure safety. Covariance steering is a particularly robust approach to this problem since it plans not just a path but how the robot’s confidence in its own state should evolve as it moves. Previous methods only guarantee completeness for LTI systems under constant noise and disturbance, which are assumptions that rarely hold in practice. This project removes both assumptions, requiring new theoretical conditions and algorithmic development, since covariance propagation itself becomes time-dependent and a plan valid under one noise level can become infeasible if noise increases or overly conservative if it decreases. Moving to an online planner also raises a computational challenge, since noise must now be estimated from sensor data in real time. Map generation and local optimization, which currently take minutes, must instead run within the timescale of the robot’s control loop, requiring them to be sub-second. I will implement and validate the algorithm first in simulation, then on hardware such as a quadrotor running fully onboard on embedded compute.

Safety and planning under uncertainty are fields I am interested in, and this project connects to my previous work. I am excited to work closely with mentors who have direct experience in this area and can share their insights. SuperUROP is also a valuable chance to get experience in the publication process, from developing results to writing them up, as I think about pursuing research and graduate school.