<p>Object detection is mostly driven by the successes of detection algorithms in world-famous object detection benchmarks like PASCAL-VOC and MS-COCO, which are object centric datasets where most objects are vertical (potted plants, humans, horses, etc.) and thus data augmentation with left-right flips is often sufficient (for all we know data augmentation with rotated images like upside-down flips could even hurt detection performance).<br>
Every year the entire community adopts the base algorithmic structure of the winning solution and build on it (I am exaggerating a bit to prove a point but not so much).  </p>

<p>Interestingly other less widely known topics like oriented text detections and oriented vehicle detections in aerial imagery both need rotation invariant features and rotation equivariant detection pipelines (like in both articles from Cheng you mentioned). </p>

<p>If you want to find literature and code in this area you need to dive in these two domains. I can already give you a few pointers like the <a href="https://arxiv.org/pdf/1711.10398.pdf" rel="noreferrer">DOTA</a> challenge for aerial imagery or the <a href="https://arxiv.org/abs/1506.03184" rel="noreferrer">ICDAR challenges</a> for oriented text detections.  </p>

<p>As @Marcin Mozejko said, CNN are by nature translation invariant and not rotation invariant. It is an open problem how to incorporate perfect rotation invariance the few articles that deal with it have yet to become standards even though <a href="https://arxiv.org/pdf/1604.06720.pdf" rel="noreferrer">some</a> <a href="https://arxiv.org/abs/1711.07289" rel="noreferrer">of them</a> seem promising. 
My personal favorite for detection is the modification of Faster R-CNN recently proposed by <a href="https://arxiv.org/abs/1703.01086" rel="noreferrer">Ma</a>.   </p>

<p>I hope that this direction of research will be investigated more and more once people will get fed up of MS-COCO and VOC.</p>

<p>What you could try is take a state-of-the-art detector trained on MS-COCO like <a href="https://github.com/tensorflow/models/tree/master/research/object_detection" rel="noreferrer">Faster R-CNN with NASNet from TF detection API</a> and see how it performs wrt rotating the test image, in my opinion it would be far from rotation invariant.</p>
Why rotation-invariant neural networks are not used in winners of the popular competitions?
<p>As known, modern most popular CNN (convolutional neural network): VGG/ResNet (FasterRCNN), SSD, Yolo, Yolo v2, DenseBox, DetectNet - are not rotate invariant: <a href="https://stackoverflow.com/questions/40952163/are-modern-cnn-convolutional-neural-network-as-detectnet-rotate-invariant">Are modern CNN (convolutional neural network) as DetectNet rotate invariant?</a></p>

<p>Also known, that there are several neural networks with rotate-invariance object detection:</p>

<ol>
<li><p>Rotation-Invariant Neoperceptron 2006 (<a href="https://www.researchgate.net/profile/Beat_Fasel/publication/224649475_Rotation-Invariant_Neoperceptron/links/02e7e53859a00a588b000000.pdf" rel="noreferrer">PDF</a>): <a href="https://www.researchgate.net/publication/224649475_Rotation-Invariant_Neoperceptron" rel="noreferrer">https://www.researchgate.net/publication/224649475_Rotation-Invariant_Neoperceptron</a></p></li>
<li><p>Learning rotation invariant convolutional filters for texture classification 2016 (<a href="https://arxiv.org/pdf/1604.06720v2" rel="noreferrer">PDF</a>): <a href="https://arxiv.org/abs/1604.06720" rel="noreferrer">https://arxiv.org/abs/1604.06720</a></p></li>
<li><p>RIFD-CNN: Rotation-Invariant and Fisher Discriminative Convolutional Neural Networks for Object Detection 2016 (<a href="http://www.cv-foundation.org/openaccess/content_cvpr_2016/papers/Cheng_RIFD-CNN_Rotation-Invariant_and_CVPR_2016_paper.pdf" rel="noreferrer">PDF</a>): <a href="http://www.cv-foundation.org/openaccess/content_cvpr_2016/html/Cheng_RIFD-CNN_Rotation-Invariant_and_CVPR_2016_paper.html" rel="noreferrer">http://www.cv-foundation.org/openaccess/content_cvpr_2016/html/Cheng_RIFD-CNN_Rotation-Invariant_and_CVPR_2016_paper.html</a></p></li>
<li><p>Encoded Invariance in Convolutional Neural Networks 2014 (<a href="http://theorycenter.cs.uchicago.edu/REU/2014/final-papers/sauder.pdf" rel="noreferrer">PDF</a>)</p></li>
<li><p>Rotation-invariant convolutional neural networks for galaxy morphology prediction (<a href="https://arxiv.org/pdf/1503.07077v1" rel="noreferrer">PDF</a>): <a href="https://arxiv.org/abs/1503.07077" rel="noreferrer">https://arxiv.org/abs/1503.07077</a></p></li>
<li><p>Learning Rotation-Invariant Convolutional Neural Networks for Object Detection in VHR Optical Remote Sensing Images 2016: <a href="http://ieeexplore.ieee.org/document/7560644/" rel="noreferrer">http://ieeexplore.ieee.org/document/7560644/</a></p></li>
</ol>

<p>We know, that in such image-detection competitions as: IMAGE-NET, MSCOCO, PASCAL VOC - used networks ensembles (simultaneously some neural networks). Or networks ensembles in single net such as ResNet (<a href="https://arxiv.org/abs/1605.06431" rel="noreferrer">Residual Networks Behave Like Ensembles of Relatively Shallow Networks</a>)</p>

<p>But are used rotation invariant network ensembles in winners like as MSRA, and if not, then why? Why in ensemble the additional rotation-invariant network does not add accuracy to detect certain objects such as aircraft objects - which images is done at a different angles of rotation? </p>

<p>It can be:</p>

<ul>
<li><p>aircraft objects which are photographed from the ground 
<a href="https://i.stack.imgur.com/s9C7w.jpg" rel="noreferrer"><img src="https://i.stack.imgur.com/s9C7w.jpg" alt="enter image description here"></a></p></li>
<li><p>or ground objects which are photographed from the air
<a href="https://i.stack.imgur.com/ICqUL.jpg" rel="noreferrer"><img src="https://i.stack.imgur.com/ICqUL.jpg" alt="enter image description here"></a></p></li>
</ul>

<p>Why rotation-invariant neural networks are not used in winners of the popular object-detection competitions?</p>