No sampled gradients for high-speed drone flight: APG-Planner trains in about 30 minutes on one GPU and hits 11 m/s in real flight
Synopsis
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.
Interpretation
A vision-based high-speed planner can now be trained in about 30 minutes on a single GPU and fly a real quadrotor at a peak speed of about 11 m/s. Earlier learned planners followed imitation learning, limited by expert-trajectory quality and coverage, or guidance learning, whose gradients stay local to each planning decision; model-free policy-gradient methods estimate gradients from samples, giving high variance and sample-intensive training. In the Flightmare simulator, under identical initial conditions and collision criteria against optimization-based EGO, imitation-based AGILE and guidance-based YOPO, APG-Planner reaches comparable or higher success rates on sparse and dense forest maps while producing lower-snap trajectories, particularly at higher speeds.
Training no longer needs a low-level dynamics model, because each planned trajectory segment itself carries the state from one replanning step to the next. Earlier analytic-policy-gradient work propagated states through a differentiable dynamics simulator calibrated with real flight data, including parameters such as aerodynamic drag, so each new vehicle required recalibration. Position, heading and finitely many derivatives serve as flat outputs; a quintic polynomial is solved from the current state and the policy's terminal conditions, and the flatness map analytically reconstructs the state at each replanning instant. In the ablation, full APG averages about 8.16 and 7.47 m/s at 94% and 92% success on sparse and dense maps, while the variant blocking cross-step gradients reaches only about 2.46 and 2.05 m/s.
Swapping the flatness model and network output bounds lets the same training framework move to another differentially flat robot. Beyond quadrotors, the transfer recipe is to model the target platform as a differentially flat system and redefine the state transition in terms of that platform's flat outputs. A Clearpath Jackal skid-steer ground robot is modeled as a unicycle with planar position as the flat output, and it navigates around natural obstacles in a real forest while tracking collision-free trajectories.
Perspective
The demonstrated scope is a comparison on sparse and dense forest maps in the Flightmare simulator, real quadrotor flight with a Jetson Orin NX and an OAK-D Pro Wide camera, and forest experiments with a Jackal ground robot; planning runs onboard at a fixed rate and trajectories are tracked by a separate geometric or PD controller.
The flatness-based state transitions used in training assume accurate trajectory tracking; the effect of tracking error in real flight is suggested to be mitigated by trajectory smoothness and replanning from updated state estimates, but that explanation is offered tentatively, and the ablation variant without cross-step gradients keeps high success rates while its mean speed drops markedly.