# Trajectory Planning

Vision-based high-speed trajectory planners are usually trained with model-free reinforcement learning, whose sampled policy-gradient estimates are noisy and slow to train. APG-Planner instead uses analytic policy gradients: differential flatness analytically reconstructs vehicle states from planned trajectories, chaining successive replans into a differentiable episode whose loss is backpropagated. After about 30 minutes on a single GPU, it matches or beats EGO, AGILE and YOPO in simulation and reaches a peak speed of about 11 m/s in real quadrotor flight.

Vision-based high-speed trajectory planners are usually trained with model-free reinforcement learning, whose sampled policy-gradient estimates are noisy and slow to train. APG-Planner instead uses analytic policy gradients: differential flatness analytically reconstructs vehicle states from planned trajectories, chaining successive replans into a differentiable episode whose loss is backpropagated. After about 30 minutes on a single GPU, it matches or beats EGO, AGILE and YOPO in simulation and reaches a peak speed of about 11 m/s in real quadrotor flight.