Research

Provably correct, real-time algorithms for autonomous dynamical systems.

Research areas

Trajectory Optimization

We study onboard computation of optimal trajectories for systems with nonconvex dynamics and constraints. Lossless convexification shows that selected nonconvex optimal control problems can be solved exactly through convex relaxations. Examples include fuel-optimal planetary landing with minimum-thrust and pointing constraints. Successive convexification (SCvx) extends the approach to nonlinear dynamics, including recent guarantees for continuous-time constraint satisfaction.

Convex Optimization Algorithms

Flight-grade autonomy needs solvers with predictable runtime and limited memory use. The lab designs first-order methods and conic solvers for embedded platforms. QOCO, an open-source quadratic-objective conic optimizer, is one example.

Robust Control

Real systems face disturbances, model uncertainty, and actuation limits. The lab develops feedback synthesis methods that preserve constraint satisfaction under uncertainty. One example is robust fuel-optimal trajectory planning with feedback control.

Optimal Recursive Decision-Making

Many autonomy problems are sequential. Current decisions change what will be feasible later. The lab formulates recursive decision-making problems with temporal and logical specifications, then studies convex formulations that make optimal policies computationally tractable.

Markov Decision Processes

For large-scale stochastic systems, the lab studies density control and policy synthesis on Markov decision processes. Spacecraft and vehicle swarms are the motivating cases. The goal is probabilistic guidance with safety and convergence guarantees.