Most autonomous vehicles exhibit very complex dynamics at high speeds. For example, a quadcopter aerial vehicle will experience complex aerodynamics, battery electrochemistry, and actuator dynamics. This project utilizes data-driven approaches to design very fast trajectories, accounting for these factors by optimizing for them during a set of carefully selected experiments.

This project aims to utilize data-driven approaches to generate high-speed trajectory for super-vehicle, such as quadrotor. This is challenging since it requires a precise modeling of the dynamic feasibility constraints which comes from nonlinear aerodynamics, state estimation error, or actuation delay, or battery capacity. Unfortunately, precise modeling of these constraints is only possible through risky real-world experiments. Recently, we made a Bayes-Opt framework to efficiently train a realistic vehicle model by combining multiple information sources such as analytical approximation, numerical simulation, and real-world flight experiments.

**Bayesian optimization** is a class of machine learning algorithms that uses for solving

optimization problems with unknown functions that are expensive to evaluate. It selects the next evaluation points to maximize the efficiency of modeling unknown functions to minimize the number of experiments required to solve the problem. **Multi-fidelity optimization** combines different fidelities of evaluations to minimize the cost of risky experiments. For instance, low-fidelity evaluations such as simulation or expert’s opinion can be used to reduce the number of expensive real-world experiments. Combining these two ideas, we could model the quadrotor’s dynamics model accurately with limited amounts of real-world experiments.

For instance, the method can utilize both low-fidelity and high-fidelity simulations to model the (unknown) constraints for the dynamic feasibility of a trajectory. Here is an illustrative example involving a trajectory with two segments.

Our trajectory optimization framework, called Bayes-Opt, iteratively builds a surrogate model of feasibility constraints using low-fidelity and high-fidelity samples. In this case, low-fidelity samples may include simulations of various fidelity, while high-fidelity samples correspond to the flight experiments in the laboratory. At each iteration, a new data point and fidelity is selected using the Bayesian optimization method.

The increasing interest in autonomous drone racing competition highlights the need for time-optimal trajectory that fully exploits the capabilities of the vehicle. The traditional method utilizes the vehicle's ideal dynamics model to generate racing trajectories. This implies if we have a more accurate dynamics model that takes into account real-world phenomena such as nonlinear aerodynamics, state estimation error, or actuation delay, we can generate faster trajectories. Below are some examples of trajectory optimization using our method, showing improvements from the first iteration to the last.