A Machine-Learning Approach for Time-Optimal Trajectory Generation for UAV's

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This paper presents a data-driven approach towards time-optimal trajectory generation for Unmanned Aerial Vehicles (UAV's) using a machine-learned trajectory generation mechanism for point-to-point time-optimal trajectories on-the-fly. To train this machine-learned black box trajectory generator off-line, a model-based optimization problem is first constructed for point-to-point time-optimal trajectory generation, with physical constraints on inputs, states, and rates. The formulated optimization problem is then solved off-line for a range of initial and terminal flight states to generate point-to-point data-sets that consist of the optimal state and input trajectories. This information is compressed by parameterizing the input and state trajectories using a set of basis functions. This data is then used to train the neural network-based trajectory planner. The output of the neural network is the basis function coefficient sets for the state and input trajectories (and the total flight time) which can then be used to reconstruct the flight trajectory. Once the neural network is trained, the data-driven on-board trajectory generator is ready to be deployed on the UAV for on-board planning. This approach is demonstrated for two scenarios: (1) the input to the neural network being the initial and terminal flight states and (2) the input to the neural network being initial and terminal flight states as well as physical constraints. To validate the performance of the machine-learned black-box trajectory generator, the root mean squared error between the neural network generated trajectories and the trajectories obtained from solving the optimization problem directly is statistically evaluated. These trajectories are also tested for violation of path constraints (which are not included explicitly in the training or input to the black box planner) by evaluating the mean constraint violation for each path-constrained variable.