Efficient and Guaranteed-Safe Non-Convex Trajectory Optimization with
  Constrained Diffusion Model
Anjian Li Zihan Ding Adji Bousso Dieng Ryne Beeson
Trajectory optimization in robotics poses a challenging non-convex problem
due to complex dynamics and environmental settings. Traditional numerical
optimization methods are time-consuming in finding feasible solutions, whereas
data-driven approaches lack safety guarantees for the output trajectories. In
this paper, we introduce a general and fully parallelizable framework that
combines diffusion models and numerical solvers for non-convex trajectory
optimization, ensuring both computational efficiency and constraint
satisfaction. A novel constrained diffusion model is proposed with an
additional constraint violation loss for training. It aims to approximate the
distribution of locally optimal solutions while minimizing constraint
violations during sampling. The samples are then used as initial guesses for a
numerical solver to refine and derive final solutions with formal verification
of feasibility and optimality. Experimental evaluations on three tasks over
different robotics domains verify the improved constraint satisfaction and
computational efficiency with 4$\times$ to 22$\times$ acceleration using our
proposed method, which generalizes across trajectory optimization problems and
scales well with problem complexity.