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

Time-Optimal Online Replanning for Agile Quadrotor Flight

In this letter, we tackle the problem of flying a quadrotor using time-optimal control policies that can be replanned online when the environment changes or when encountering unknown disturbances. This problem is challenging as the time-optimal trajectories that consider the full quadrotor dynamics are computationally expensive to generate, on the order of minutes or even hours. We introduce a sampling-based method for efficient generation of time-optimal paths of a point-mass model. These paths are then tracked using a Model Predictive Contouring Control approach that considers the full quadrotor dynamics and the single rotor thrust limits. Our combined approach is able to run in real-time, being the first time-optimal method that is able to adapt to changes on-the-fly . We showcase our approach’s adaption capabilities by flying a quadrotor at more than 60 km/h in a racing track where gates are moving. Additionally, we show that our online replanning approach can cope with strong disturbances caused by winds of up to 68 km/h

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 substantially 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, with quadrotor speeds of up to 42kmh−1 and accelerations of 3.6 g

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

Energy-aware Multi-UAV Coverage Mission Planning with Optimal Speed of Flight

This paper tackles the problem of planning minimum-energy coverage paths for multiple UAVs. The addressed Multi-UAV Coverage Path Planning (mCPP) is a crucial problem for many UAV applications such as inspection and aerial survey. However, the typical path-length objective of existing approaches does not directly minimize the energy consumption, nor allows for constraining energy of individual paths by the battery capacity. To this end, we propose a novel mCPP method that uses the optimal flight speed for minimizing energy consumption per traveled distance and a simple yet precise energy consumption estimation algorithm that is utilized during the mCPP planning phase. The method decomposes a given area with boustrophedon decomposition and represents the mCPP as an instance of Multiple Set Traveling Salesman Problem with a minimum energy objective and energy consumption constraint. The proposed method is shown to outperform state-of-the-art methods in terms of computational time and energy efficiency of produced paths. The experimental results show that the accuracy of the energy consumption estimation is on average 97% compared to real flight consumption. The feasibility of the proposed method was verified in a real-world coverage experiment with two UAVs.Comment: in IEEE Robotics and Automation Letter