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General pros and cons of Euler angles versus quaternions 

General pros and cons of Euler angles versus quaternions 

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The investigation of planets, moons and small bodies, including comets and asteroids can contribute substantially to our understanding of the formation and history of the solar system. In situ observations by landers play an important role in this field: for example, the Rosetta Lander Philae has been the first spacecraft to accomplish a soft touch...

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Small bodies - comets, asteroids, TNOs are relics of the planetesimals that formed during the early stages of the Solar System and thus, studying these objects is crucial for understanding the formation and evolution of the Solar System. We are currently living in the golden age for the exploration of small bodies that includes many recent and ongo...

Citations

... PyJama implements fusion filters in quaternions. The motivation for using quaternions is the data stability, considering that the rotation using Euler angles can present more errors and the occurrence of Gimbal Lock [12,13]. Thus, Complementary Filter(CF) with Gradient Descent and Gauss-Newton [6,14], Kalman Filter (KF) with Gradient Descent and Gauss-Newton [6,14], and MadgwickAHRS [5] were implemented. ...
... Structurally, the class functions use the matplotlib. In addition, users can choose to use and visualize the data with the orientation in quaternions or Euler angles, the last is the most common way to visualize joint rotations [12]. ...
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The use of inertial measurement units (IMUs) is a low-cost alternative for measuring joint angles. This study aims to present a low-cost open-source measurement system for joint angle estimation. The system is modular and has hardware and software. The hardware was developed using a low-cost IMU and microcontroller. The IMU data analysis software was developed in Python and has three fusion filters: Complementary Filter, Kalman Filter, and Madgwick Filter. Three experiments were performed for the proof of concept of the system. First, we evaluated the knee joint of Lokomat, with a predefined average range of motion (ROM) of 60∘. In the second, we evaluated our system in a real scenario, evaluating the knee of a healthy adult individual during gait. In the third experiment, we evaluated the software using data from gold standard devices, comparing the results of our software with Ground Truth. In the evaluation of the Lokomat, our system achieved an average ROM of 58.28∘, and during evaluation in a real scenario it achieved an average ROM of 44.62∘. In comparing our software with Ground Truth, we achieved a root-mean-square error of 0.04 and a mean average percentage error of 2.95%. These results encourage the use of this system in other scenarios.
... A safe landing is the last and the key part of a flight, which is one of the challenges for flying animals, 1-3 aircraft, 4 or spacecraft 5 returning to the ground. Previous studies have focused on the landing behaviour, during which, the airspeed and rate of descent are reduced as the object descends at a low enough rate to allow for a gentle touchdown; touchdown is usually accomplished by reduced thrust or increased drag using visual and antennae-derived cues, 6 flaps, 3 or landing gear. ...
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Whether for insects or for aircrafts, landing is one of the indispensable links in the verification of airworthiness safety. The mechanisms by which insects achieve a fast and stable landing remain unclear. An intriguing example is provided by honeybees (Apis mellifera ligustica), which use the swinging motion of their abdomen to dissipate residual flying energy and to achieve a smooth, stable, and quick landing. By using a high-speed camera, we observed that touchdown is initiated by honeybees extending their front legs or antennae and then landing softly on a wall. After touchdown, they swing the rest of their bodies until all flying energy is dissipated. We suggested a simplified model with mass-spring dampers for the body of the honeybee and revealed the mechanism of flying energy transfer and dissipation in detail. Results demonstrate that body translation and abdomen swinging help honeybees dissipate residual flying energy and orchestrate smooth landings. The initial kinetic energy of flying is transformed into the kinetic energy of the abdomen's rotary movement. Then, the kinetic energy of rotary movement is converted into thermal energy during the swinging cycle. This strategy provides more insight into the mechanism of insect flying, which further inspires better design on aerial vehicle with better landing performance.
... The main advantage is the gain in computational stability which depends now on the chosen value of v d . This is the friction model available in commercial codes such as DCAP [46] and SimPack [56]. ...
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Friction force models play a fundamental role for simulation of mechanical systems. Their choice affects the matching of numerical results with physically observed behavior. Friction is a complex phenomenon depending on many physical parameters and working conditions and none of the available models can claim general validity. This paper focuses the attention on well known friction models and offers a review and comparison based on numerical efficiency. However, it should be acknowledged that each model has its own distinctive pros and cons. Suitability of the model depends on physical and operating conditions. Features such as the capability to replicate stiction, Stribeck effect and pre-sliding displacement are taken into account when selecting a friction formulation. For mechanical systems, the computational efficiency of the algorithm is a critical issue when a fast and responsive dynamic computation is required. This paper reports and compares eight widespread engineering friction force models. These are divided into two main categories: those based on the Coulomb approach and those established on the bristle analogy. The numerical performances and differences of each model have been monitored and compared. Three test cases are discussed: the Rabinowicz test and other two test problems casted for this occurrence.