Men of Faith: Stravinsky, Maritain and the Ideal Christian Artifex

In this paper I explore the relationship and mutual influences between Stravinsky and Maritain. Despite the connections between these two men, and the prominence which Stravinsky at least still holds, scholars have neglected to examine their relationship in any depth. Although there is an abundance of recent scholarship on Stravinsky, most of it concentrates on Stravinsky during his Russian period, or on the workings of Stravinsky’s serial music divorced from its religious subject matter.8 I will demonstrate how Stravinsky met the criteria of Maritain’s ideal Christian artifex by analysing Canticum Sacrum (1955) through the lens of Maritain’s philosophy. One of Stravinsky’s major religious works, Canticum Sacrum was also one of his first works to use serialism. Although it is neither neo-classical nor from the period of Stravinsky’s rededication, it demonstrates not only how Stravinsky exemplified Maritain’s ideal, but that he continued to exemplify this ideal in his later works. While neither man changed his work to comply with the beliefs of the other, both Stravinsky and Maritain used each others’ writings – both musical and philosophical – to support and explain their methods, ideas and inspirations. Maritain’s enshrinement of Stravinsky as the prime living example of his artistic ideal boosted the popularity of his own philosophy, and Stravinsky ultimately lived up to the role of the ideal Christian artifex with pleasure, publicly describing himself in Maritain’s terms and finding a method of worship through his art that required no overt prostrations, only humble belief

Men of Faith: Stravinsky, Maritain and the Ideal Christian Artifex

In this paper I explore the relationship and mutual influences between Stravinsky and Maritain. Despite the connections between these two men, and the prominence which Stravinsky at least still holds, scholars have neglected to examine their relationship in any depth. Although there is an abundance of recent scholarship on Stravinsky, most of it concentrates on Stravinsky during his Russian period, or on the workings of Stravinsky’s serial music divorced from its religious subject matter.8 I will demonstrate how Stravinsky met the criteria of Maritain’s ideal Christian artifex by analysing Canticum Sacrum (1955) through the lens of Maritain’s philosophy. One of Stravinsky’s major religious works, Canticum Sacrum was also one of his first works to use serialism. Although it is neither neo-classical nor from the period of Stravinsky’s rededication, it demonstrates not only how Stravinsky exemplified Maritain’s ideal, but that he continued to exemplify this ideal in his later works. While neither man changed his work to comply with the beliefs of the other, both Stravinsky and Maritain used each others’ writings – both musical and philosophical – to support and explain their methods, ideas and inspirations. Maritain’s enshrinement of Stravinsky as the prime living example of his artistic ideal boosted the popularity of his own philosophy, and Stravinsky ultimately lived up to the role of the ideal Christian artifex with pleasure, publicly describing himself in Maritain’s terms and finding a method of worship through his art that required no overt prostrations, only humble belief

Minimum-Time Quadrotor Waypoint Flight in Cluttered Environments

We tackle the problem of planning a minimum-time trajectory for a quadrotor over a sequence of specified waypoints in the presence of obstacles while exploiting the full quadrotor dynamics. This problem is crucial for autonomous search and rescue and drone racing scenarios but was, so far, unaddressed by the robotics community \emph{in its entirety} due to the challenges of minimizing time in the presence of the non-convex constraints posed by collision avoidance. Early works relied on simplified dynamics or polynomial trajectory representations that did not exploit the full actuator potential of a quadrotor and, thus, did not aim at minimizing time. We address this challenging problem by using a hierarchical, sampling-based method with an incrementally more complex quadrotor model. Our method first finds paths in different topologies to guide subsequent trajectory search for a kinodynamic point-mass model. Then, it uses an asymptotically-optimal, kinodynamic sampling-based method based on a full quadrotor model on top of the point-mass solution to find a feasible trajectory with a time-optimal objective. The proposed method is shown to outperform all related baselines in cluttered environments and is further validated in real-world flights at over 60km/h in one of the world's largest motion capture systems. We release the code open source.Comment: Accepted in IEEE Robotics and Automation Letter

CTopPRM: Clustering Topological PRM for Planning Multiple Distinct Paths in 3D Environments

In this paper, we propose a new method called Clustering Topological PRM (CTopPRM) for finding multiple homotopically distinct paths in 3D cluttered environments. Finding such distinct paths, e.g., going around an obstacle from a different side, is useful in many applications. Among others, using multiple distinct paths is necessary for optimization-based trajectory planners where found trajectories are restricted to only a single homotopy class of a given path. Distinct paths can also be used to guide sampling-based motion planning and thus increase the effectiveness of planning in environments with narrow passages. Graph-based representation called roadmap is a common representation for path planning and also for finding multiple distinct paths. However, challenging environments with multiple narrow passages require a densely sampled roadmap to capture the connectivity of the environment. Searching such a dense roadmap for multiple paths is computationally too expensive. Therefore, the majority of existing methods construct only a sparse roadmap which, however, struggles to find all distinct paths in challenging environments. To this end, we propose the CTopPRM which creates a sparse graph by clustering an initially sampled dense roadmap. Such a reduced roadmap allows fast identification of homotopically distinct paths captured in the dense roadmap. We show, that compared to the existing methods the CTopPRM improves the probability of finding all distinct paths by almost 20% in tested environments, during same run-time. The source code of our method is released as an open-source package.Comment: in IEEE Robotics and Automation Letter

Learning Minimum-Time Flight in Cluttered Environments

We tackle the problem of minimum-time flight for a quadrotor through a sequence of waypoints in the presence of obstacles while exploiting the full quadrotor dynamics. Early works relied on simplified dynamics or polynomial trajectory representations that did not exploit the full actuator potential of the quadrotor, and, thus, resulted in suboptimal solutions. Recent works can plan minimum-time trajectories; yet, the trajectories are executed with control methods that do not account for obstacles. Thus, a successful execution of such trajectories is prone to errors due to model mismatch and in-flight disturbances. To this end, we leverage deep reinforcement learning and classical topological path planning to train robust neural-network controllers for minimum-time quadrotor flight in cluttered environments. The resulting neural network controller demonstrates significantly better performance of up to 19% over state-of-the-art methods. More importantly, the learned policy solves the planning and control problem simultaneously online to account for disturbances, thus achieving much higher robustness. As such, the presented method achieves 100% success rate of flying minimum-time policies without collision, while traditional planning and control approaches achieve only 40%. The proposed method is validated in both simulation and the real world

The MRS UAV System: Pushing the Frontiers of Reproducible Research, Real-world Deployment, and Education with Autonomous Unmanned Aerial Vehicles

We present a multirotor Unmanned Aerial Vehicle control (UAV) and estimation system for supporting replicable research through realistic simulations and real-world experiments. We propose a unique multi-frame localization paradigm for estimating the states of a UAV in various frames of reference using multiple sensors simultaneously. The system enables complex missions in GNSS and GNSS-denied environments, including outdoor-indoor transitions and the execution of redundant estimators for backing up unreliable localization sources. Two feedback control designs are presented: one for precise and aggressive maneuvers, and the other for stable and smooth flight with a noisy state estimate. The proposed control and estimation pipeline are constructed without using the Euler/Tait-Bryan angle representation of orientation in 3D. Instead, we rely on rotation matrices and a novel heading-based convention to represent the one free rotational degree-of-freedom in 3D of a standard multirotor helicopter. We provide an actively maintained and well-documented open-source implementation, including realistic simulation of UAV, sensors, and localization systems. The proposed system is the product of years of applied research on multi-robot systems, aerial swarms, aerial manipulation, motion planning, and remote sensing. All our results have been supported by real-world system deployment that shaped the system into the form presented here. In addition, the system was utilized during the participation of our team from the CTU in Prague in the prestigious MBZIRC 2017 and 2020 robotics competitions, and also in the DARPA SubT challenge. Each time, our team was able to secure top places among the best competitors from all over the world. On each occasion, the challenges has motivated the team to improve the system and to gain a great amount of high-quality experience within tight deadlines.Comment: 28 pages, 20 figures, submitted to Journal of Intelligent & Robotic Systems (JINT), for the provided open-source software see http://github.com/ctu-mr