This supplementary document is organized as follows. We provide details in terms of the concept of'solution' to an SDE, how we use a finite-differences As illustrated in Figure 1 in the main paper, the concept of a'solution' to an SDE is broader than that of This is what is done in this paper. We can now interpret Eq. (7) through these finite difference The model which we call a'GP-SDE' model in the main paper has appeared in various forms in literature before. It directly resembles a'random' ODE model, where the random field Figure 1 in the main paper, just providing further examples from the test set. For the timing experiments in Sec. 3, we constructed a setup that allowed us to control the approximation error.

This supplementary document is organized as follows. We provide details in terms of the concept of'solution' to an SDE, how we use a finite-differences As illustrated in Figure 1 in the main paper, the concept of a'solution' to an SDE is broader than that of This is what is done in this paper. We can now interpret Eq. (7) through these finite difference The model which we call a'GP-SDE' model in the main paper has appeared in various forms in literature before. It directly resembles a'random' ODE model, where the random field Figure 1 in the main paper, just providing further examples from the test set. For the timing experiments in Sec. 3, we constructed a setup that allowed us to control the approximation error.

Reinforcement learning (RL) has achieved outstanding success in complex robot control tasks, such as drone racing, where the RL agents have outperformed human champions in a known racing track. However, these agents fail in unseen track configurations, always requiring complete retraining when presented with new track layouts. This work aims to develop RL agents that generalize effectively to novel track configurations without retraining. The naive solution of training directly on a diverse set of track layouts can overburden the agent, resulting in suboptimal policy learning as the increased complexity of the environment impairs the agent's ability to learn to fly. To enhance the generalizability of the RL agent, we propose an adaptive environment-shaping framework that dynamically adjusts the training environment based on the agent's performance. We achieve this by leveraging a secondary RL policy to design environments that strike a balance between being challenging and achievable, allowing the agent to adapt and improve progressively. Using our adaptive environment shaping, one single racing policy efficiently learns to race in diverse challenging tracks. Experimental results validated in both simulation and the real world show that our method enables drones to successfully fly complex and unseen race tracks, outperforming existing environment-shaping techniques. Project page: http://rpg.ifi.uzh.ch/env_as_policy/index.html

Autonomous drone racing requires powerful perception, planning, and control and has become a benchmark and test field for autonomous, agile flight. Existing work usually assumes static race tracks with known maps, which enables offline planning of time-optimal trajectories, performing localization to the gates to reduce the drift in visual-inertial odometry (VIO) for state estimation or training learning-based methods for the particular race track and operating environment. In contrast, many real-world tasks like disaster response or delivery need to be performed in unknown and dynamic environments. To close this gap and make drone racing more robust against unseen environments and moving gates, we propose a control algorithm that does not require a race track map or VIO and uses only monocular measurements of the line of sight (LOS) to the gates. For this purpose, we adopt the law of proportional navigation (PN) to accurately fly through the gates despite gate motions or wind. We formulate the PN-informed vision-based control problem for drone racing as a constrained optimization problem and derive a closed-form optimal solution. We demonstrate through extensive simulations and real-world experiments that our method can navigate through moving gates at high speeds while being robust to different gate movements, model errors, wind, and delays.

This document presents the design of an autonomous car developed by the UruBots team for the 2024 FIRA Autonomous Cars Race Challenge. The project involves creating an RC-car sized electric vehicle capable of navigating race tracks with in an autonomous manner. It integrates mechanical and electronic systems alongside artificial intelligence based algorithms for the navigation and real-time decision-making. The core of our project include the utilization of an AI-based algorithm to learn information from a camera and act in the robot to perform the navigation. We show that by creating a dataset with more than five thousand samples and a five-layered CNN we managed to achieve promissing performance we our proposed hardware setup. Overall, this paper aims to demonstrate the autonomous capabilities of our car, highlighting its readiness for the 2024 FIRA challenge, helping to contribute to the field of autonomous vehicle research.

Existing approaches to trajectory planning for autonomous racing employ sampling-based methods, generating numerous jerk-optimal trajectories and selecting the most favorable feasible trajectory based on a cost function penalizing deviations from an offline-calculated racing line. While successful on oval tracks, these methods face limitations on complex circuits due to the simplistic geometry of jerk-optimal edges failing to capture the complexity of the racing line. Additionally, they only consider two-dimensional tracks, potentially neglecting or surpassing the actual dynamic potential. In this paper, we present a sampling-based local trajectory planning approach for autonomous racing that can maintain the lap time of the racing line even on complex race tracks and consider the race track's three-dimensional effects. In simulative experiments, we demonstrate that our approach achieves lower lap times and improved utilization of dynamic limits compared to existing approaches. We also investigate the impact of online racing line generation, in which the time-optimal solution is planned from the current vehicle state for a limited spatial horizon, in contrast to a closed racing line calculated offline. We show that combining the sampling-based planner with the online racing line generation can significantly reduce lap times in multi-vehicle scenarios.

We propose a novel B-spline trajectory optimization method for autonomous racing. We consider the unavailability of sophisticated race car and race track dynamics in early-stage autonomous motorsports development and derive methods that work with limited dynamics data and additional conservative constraints. We formulate a minimum-curvature optimization problem with only the spline control points as optimization variables. We then compare the current state-of-the-art method with our optimization result, which achieves a similar level of optimality with a 90% reduction on the decision variable dimension, and in addition offers mathematical smoothness guarantee and flexible manipulation options. We concurrently reduce the problem computation time from seconds to milliseconds for a long race track, enabling future online adaptation of the previously offline technique.

In drone racing, the time-minimum trajectory is affected by the drone's capabilities, the layout of the race track, and the configurations of the gates (e.g., their shapes and sizes). However, previous studies neglect the configuration of the gates, simply rendering drone racing a waypoint-passing task. This formulation often leads to a conservative choice of paths through the gates, as the spatial potential of the gates is not fully utilized. To address this issue, we present a time-optimal planner that can faithfully model gate constraints with various configurations and thereby generate a more time-efficient trajectory while considering the single-rotor-thrust limits. Our approach excels in computational efficiency which only takes a few seconds to compute the full state and control trajectories of the drone through tracks with dozens of different gates. Extensive simulations and experiments confirm the effectiveness of the proposed methodology, showing that the lap time can be further reduced by taking into account the gate's configuration. We validate our planner in real-world flights and demonstrate super-extreme flight trajectory through race tracks.

Social media users hurled criticism at Microsoft this week for what many thought was an AI-generated obituary for NBA player Brandon Hunter on its website MSN. The controversy began after the obituary -- which had a headline that read "Brandon Hunter useless at 42" written by "Editor" -- appeared on the Microsoft-owned platform after Hunter's death on Tuesday. The obituary goes on to refer to the former Boston Celtics and Orlando Magic player having been "handed away on the age of 42" and claimed he "performed in 67 video games over two seasons and achieved a career-high of 17 factors in a recreation in opposition to the Milwaukee Bucks in 2004." The post appeared to follow a similar format to a story on TMZ Sports, Futurism noted, "albeit with altered punctuation and a use of synonyms so liberal that the result is essentially incomprehensible." You can compare both the obituary containing the error and the TMZ Sports story here.

With the rising popularity of autonomous navigation research, Formula Student (FS) events are introducing a Driverless Vehicle (DV) category to their event list. This paper presents the initial investigation into utilising Deep Reinforcement Learning (RL) for end-to-end control of an autonomous FS race car for these competitions. We train two state-of-the-art RL algorithms in simulation on tracks analogous to the full-scale design on a Turtlebot2 platform. The results demonstrate that our approach can successfully learn to race in simulation and then transfer to a real-world racetrack on the physical platform. Finally, we provide insights into the limitations of the presented approach and guidance into the future directions for applying RL toward full-scale autonomous FS racing.