In this work we present a real-time approach for local trajectory replanning for MAVs. Current trajectory generation methods for multicopters achieve high success rates in cluttered environments, but assume the environment is static and require prior knowledge of the map. In our work we utilize the results of such planners and extend them with local replanning algorithm that can handle unmodeled (possibly dynamic) obstacles while keeping MAV close to the global trajectory. To make our approach real-time capable we maintain information about the environment around MAV in an occupancy grid stored in 3D circular buffer that moves together with a drone, and represent the trajectories using uniform B-splines. This representation ensures that trajectory is sufficiently smooth and at the same time allows efficient optimization.
To deal with the memory limitation, octree-based representations of the environment are used in @cite_5 @cite_19 . They store information in an efficient way by pruning the leaves of the trees that contain the same information, but the access times for each element become logarithmic in the number of nodes, instead of the constant time as in the voxel-based approaches.
@cite_19 @cite_5
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We present a deep convolutional decoder architecture that can generate volumetric 3D outputs in a compute- and memory-efficient manner by using an octree representation. The network learns to predict both the structure of the octree, and the occupancy values of individual cells. This makes it a particularly valuable technique for generating 3D shapes. In contrast to standard decoders acting on regular voxel grids, the architecture does not have cubic complexity. This allows representing much higher resolution outputs with a limited memory budget. We demonstrate this in several application domains, including 3D convolutional autoencoders, generation of objects and whole scenes from high-level representations, and shape from a single image. A geometric modeling technique called Octree Encoding is presented. Arbitrary 3-D objects can be represented to any specified resolution in a hierarchical 8-ary tree structure or “octree” Objects may be concave or convex, have holes (including interior holes), consist of disjoint parts, and possess sculptured (i.e., “free-form”) surfaces. The memory required for representation and manipulation is on the order of the surface area of the object. A complexity metric is proposed based on the number of nodes in an object's tree representation. Efficient (linear time) algorithms have been developed for the Boolean operations (union, intersection and difference), geometric operations (translation, scaling and rotation), N-dimensional interference detection, and display from any point in space with hidden surfaces removed. The algorithms require neither floating-point operations, integer multiplications, nor integer divisions. In addition, many independent sets of very simple calculations are typically generated, allowing implementation over many inexpensive high-bandwidth processors operating in parallel. Real time analysis and manipulation of highly complex situations thus becomes possible. We present OctNet, a representation for deep learning with sparse 3D data. In contrast to existing models, our representation enables 3D convolutional networks which are both deep and high resolution. Towards this goal, we exploit the sparsity in the input data to hierarchically partition the space using a set of unbalanced octrees where each leaf node stores a pooled feature representation. This allows to focus memory allocation and computation to the relevant dense regions and enables deeper networks without compromising resolution. We demonstrate the utility of our OctNet representation by analyzing the impact of resolution on several 3D tasks including 3D object classification, orientation estimation and point cloud labeling. In both the human brain and any general artificial intelligence (AI), a representation of the past is necessary to predict the future. However, perfect storage of all experiences is not possible. One possibility, utilized in many applications, is to retain information about the past in a buffer. A limitation of this approach is that although events in the buffer are represented with perfect accuracy, the resources necessary to represent information at a particular time scale go up rapidly. Here we present a neurally-plausible, compressed, scale-free memory representation we call Scale-Invariant Temporal History (SITH). This representation covers an exponentially large period of time in the past at the cost of sacrificing temporal accuracy for events further in the past. The form of this decay is scale-invariant and can be shown to be optimal in that it is able to respond to worlds with a wide range of time scales. We demonstrate the utility of this representation in learning to play a simple video game. In this environment, SITH exhibits better learning performance than a fixed-size buffer history representation. Whereas the buffer performs well as long as the temporal dependencies can be represented within the buffer, SITH performs well over a much larger range of time scales for the same amount of resources. Finally, we discuss how the application of SITH, along with other human-inspired models of cognition, could improve reinforcement and machine learning algorithms in general.