An N-Point Linear Solver for Line and Motion Estimation with Event Cameras

Event cameras respond primarily to edges--formed by strong gradients--and are thus particularly well-suited for line-based motion estimation. Recent work has shown that events generated by a single line each satisfy a polynomial constraint which describes a manifold in the space-time volume. Multiple such constraints can be solved simultaneously to recover the partial linear velocity and line parameters. In this work, we show that, with a suitable line parametrization, this system of constraints is actually linear in the unknowns, which allows us to design a novel linear solver. Unlike existing solvers, our linear solver (i) is fast and numerically stable since it does not rely on expensive root finding, (ii) can solve both minimal and overdetermined systems with more than 5 events, and (iii) admits the characterization of all degenerate cases and multiple solutions. The found line parameters are singularity-free and have a fixed scale, which eliminates the need for auxiliary constraints typically encountered in previous work. To recover the full linear camera velocity we fuse observations from multiple lines with a novel velocity averaging scheme that relies on a geometrically-motivated residual, and thus solves the problem more efficiently than previous schemes which minimize an algebraic residual. Extensive experiments in synthetic and real-world settings demonstrate that our method surpasses the previous work in numerical stability, and operates over 600 times faster.

Mitigating Motion Blur in Neural Radiance Fields with Events and Frames

Neural Radiance Fields (NeRFs) have shown great potential in novel view synthesis. However, they struggle to render sharp images when the data used for training is affected by motion blur. On the other hand, event cameras excel in dynamic scenes as they measure brightness changes with microsecond resolution and are thus only marginally affected by blur. Recent methods attempt to enhance NeRF reconstructions under camera motion by fusing frames and events. However, they face challenges in recovering accurate color content or constrain the NeRF to a set of predefined camera poses, harming reconstruction quality in challenging conditions. This paper proposes a novel formulation addressing these issues by leveraging both model- and learning-based modules. We explicitly model the blur formation process, exploiting the event double integral as an additional model-based prior. Additionally, we model the event-pixel response using an end-to-end learnable response function, allowing our method to adapt to non-idealities in the real event-camera sensor. We show, on synthetic and real data, that the proposed approach outperforms existing deblur NeRFs that use only frames as well as those that combine frames and events by +6.13dB and +2.48dB, respectively.

Learning Quadruped Locomotion Using Differentiable Simulation

While most recent advancements in legged robot control have been driven by model-free reinforcement learning, we explore the potential of differentiable simulation. Differentiable simulation promises faster convergence and more stable training by computing low-variant first-order gradients using the robot model, but so far, its use for legged robot control has remained limited to simulation. The main challenge with differentiable simulation lies in the complex optimization landscape of robotic tasks due to discontinuities in contact-rich environments, e.g., quadruped locomotion. This work proposes a new, differentiable simulation framework to overcome these challenges. The key idea involves decoupling the complex whole-body simulation, which may exhibit discontinuities due to contact, into two separate continuous domains. Subsequently, we align the robot state resulting from the simplified model with a more precise, non-differentiable simulator to maintain sufficient simulation accuracy. Our framework enables learning quadruped walking in minutes using a single simulated robot without any parallelization. When augmented with GPU parallelization, our approach allows the quadruped robot to master diverse locomotion skills, including trot, pace, bound, and gallop, on challenging terrains in minutes. Additionally, our policy achieves robust locomotion performance in the real world zero-shot. To the best of our knowledge, this work represents the first demonstration of using differentiable simulation for controlling a real quadruped robot. This work provides several important insights into using differentiable simulations for legged locomotion in the real world.

Time-Optimal Flight with Safety Constraints and Data-driven Dynamics

Time-optimal quadrotor flight is an extremely challenging problem due to the limited control authority encountered at the limit of handling. Model Predictive Contouring Control (MPCC) has emerged as a leading model-based approach for time optimization problems such as drone racing. However, the standard MPCC formulation used in quadrotor racing introduces the notion of the gates directly in the cost function, creating a multi-objective optimization that continuously trades off between maximizing progress and tracking the path accurately. This paper introduces three key components that enhance the MPCC approach for drone racing. First and foremost, we provide safety guarantees in the form of a constraint and terminal set. The safety set is designed as a spatial constraint which prevents gate collisions while allowing for time-optimization only in the cost function. Second, we augment the existing first principles dynamics with a residual term that captures complex aerodynamic effects and thrust forces learned directly from real world data. Third, we use Trust Region Bayesian Optimization (TuRBO), a state of the art global Bayesian Optimization algorithm, to tune the hyperparameters of the MPC controller given a sparse reward based on lap time minimization. The proposed approach achieves similar lap times to the best state-of-the-art RL and outperforms the best time-optimal controller while satisfying constraints. In both simulation and real-world, our approach consistently prevents gate crashes with 100\% success rate, while pushing the quadrotor to its physical limit reaching speeds of more than 80km/h.

Robotics meets Fluid Dynamics: A Characterization of the Induced Airflow around a Quadrotor

The widespread adoption of quadrotors for diverse applications, from agriculture to public safety, necessitates an understanding of the aerodynamic disturbances they create. This paper introduces a computationally lightweight model for estimating the time-averaged magnitude of the induced flow below quadrotors in hover. Unlike related approaches that rely on expensive computational fluid dynamics (CFD) simulations or time-consuming empirical measurements, our method leverages classical theory from turbulent flows. By analyzing over 9 hours of flight data from drones of varying sizes within a large motion capture system, we show that the combined flow from all propellers of the drone is well-approximated by a turbulent jet. Through the use of a novel normalization and scaling, we have developed and experimentally validated a unified model that describes the mean velocity field of the induced flow for different drone sizes. The model accurately describes the far-field airflow in a very large volume below the drone which is difficult to simulate in CFD. Our model, which requires only the drone's mass, propeller size, and drone size for calculations, offers a practical tool for dynamic planning in multi-agent scenarios, ensuring safer operations near humans and optimizing sensor placements.

Bootstrapping Reinforcement Learning with Imitation for Vision-Based Agile Flight

We combine the effectiveness of Reinforcement Learning (RL) and the efficiency of Imitation Learning (IL) in the context of vision-based, autonomous drone racing. We focus on directly processing visual input without explicit state estimation. While RL offers a general framework for learning complex controllers through trial and error, it faces challenges regarding sample efficiency and computational demands due to the high dimensionality of visual inputs. Conversely, IL demonstrates efficiency in learning from visual demonstrations but is limited by the quality of those demonstrations and faces issues like covariate shift. To overcome these limitations, we propose a novel training framework combining RL and IL's advantages. Our framework involves three stages: initial training of a teacher policy using privileged state information, distilling this policy into a student policy using IL, and performance-constrained adaptive RL fine-tuning. Our experiments in both simulated and real-world environments demonstrate that our approach achieves superior performance and robustness than IL or RL alone in navigating a quadrotor through a racing course using only visual information without explicit state estimation.

State Space Models for Event Cameras

Today, state-of-the-art deep neural networks that process event-camera data first convert a temporal window of events into dense, grid-like input representations. As such, they exhibit poor generalizability when deployed at higher inference frequencies (i.e., smaller temporal windows) than the ones they were trained on. We address this challenge by introducing state-space models (SSMs) with learnable timescale parameters to event-based vision. This design adapts to varying frequencies without the need to retrain the network at different frequencies. Additionally, we investigate two strategies to counteract aliasing effects when deploying the model at higher frequencies. We comprehensively evaluate our approach against existing methods based on RNN and Transformer architectures across various benchmarks, including Gen1 and 1 Mpx event camera datasets. Our results demonstrate that SSM-based models train 33% faster and also exhibit minimal performance degradation when tested at higher frequencies than the training input. Traditional RNN and Transformer models exhibit performance drops of more than 20 mAP, with SSMs having a drop of 3.31 mAP, highlighting the effectiveness of SSMs in event-based vision tasks.

AERIAL-CORE: AI-Powered Aerial Robots for Inspection and Maintenance of Electrical Power Infrastructures

Large-scale infrastructures are prone to deterioration due to age, environmental influences, and heavy usage. Ensuring their safety through regular inspections and maintenance is crucial to prevent incidents that can significantly affect public safety and the environment. This is especially pertinent in the context of electrical power networks, which, while essential for energy provision, can also be sources of forest fires. Intelligent drones have the potential to revolutionize inspection and maintenance, eliminating the risks for human operators, increasing productivity, reducing inspection time, and improving data collection quality. However, most of the current methods and technologies in aerial robotics have been trialed primarily in indoor testbeds or outdoor settings under strictly controlled conditions, always within the line of sight of human operators. Additionally, these methods and technologies have typically been evaluated in isolation, lacking comprehensive integration. This paper introduces the first autonomous system that combines various innovative aerial robots. This system is designed for extended-range inspections beyond the visual line of sight, features aerial manipulators for maintenance tasks, and includes support mechanisms for human operators working at elevated heights. The paper further discusses the successful validation of this system on numerous electrical power lines, with aerial robots executing flights over 10 kilometers away from their ground control stations.

Reaching the Limit in Autonomous Racing: Optimal Control versus Reinforcement Learning

A central question in robotics is how to design a control system for an agile mobile robot. This paper studies this question systematically, focusing on a challenging setting: autonomous drone racing. We show that a neural network controller trained with reinforcement learning (RL) outperformed optimal control (OC) methods in this setting. We then investigated which fundamental factors have contributed to the success of RL or have limited OC. Our study indicates that the fundamental advantage of RL over OC is not that it optimizes its objective better but that it optimizes a better objective. OC decomposes the problem into planning and control with an explicit intermediate representation, such as a trajectory, that serves as an interface. This decomposition limits the range of behaviors that can be expressed by the controller, leading to inferior control performance when facing unmodeled effects. In contrast, RL can directly optimize a task-level objective and can leverage domain randomization to cope with model uncertainty, allowing the discovery of more robust control responses. Our findings allowed us to push an agile drone to its maximum performance, achieving a peak acceleration greater than 12 times the gravitational acceleration and a peak velocity of 108 kilometers per hour. Our policy achieved superhuman control within minutes of training on a standard workstation. This work presents a milestone in agile robotics and sheds light on the role of RL and OC in robot control.

Flymation: Interactive Animation for Flying Robots

Trajectory visualization and animation play critical roles in robotics research. However, existing data visualization and animation tools often lack flexibility, scalability, and versatility, resulting in limited capability to fully explore and analyze flight data. To address this limitation, we introduce Flymation, a new flight trajectory visualization and animation tool. Built on the Unity3D engine, Flymation is an intuitive and interactive tool that allows users to visualize and analyze flight data in real time. Users can import data from various sources, including flight simulators and real-world data, and create customized visualizations with high-quality rendering. With Flymation, users can choose between trajectory snapshot and animation; both provide valuable insights into the behavior of the underlying autonomous system. Flymation represents an exciting step toward visualizing and interacting with large-scale data in robotics research.