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4

Let me put homotopy into the context of planning algorithms Suppose you want to get from point A to point B. Clearly, the easiest way is to traverse a straight line. But if there is an obstacle in the way of this straight line path, what should you do? If you want to obtain the "optimal" path (e.g. traversing the least total distance to the goal), you ...


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The main problem with motion planning is the time-dimension. Not only that the UAV can move up, down, forward or backward, but the motion is also defined along the time-axis. A motion plan like "up, up, down" is fundamental different then "up, down, up". After few steps, the number of possibilities grows exponential. Even on simple examples like quadrotor ...


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I would argue, that it is not graph search. In the implementation, you keep all the nodes in a flat list and check which of the nodes is closest to the sampled point. As all nodes are checked, this might be seen as a brute-force graph search, but in the implementation is just for loop iterating though all the points in a list. The goal check is done for the ...


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The steps you have identified are correct. You will need an IK solver if you want to plan in Cartesian space. Cyclic Coordinate Descent is one OK option if you always solve for points which are close to eachother. However, I would advise to look at Unity IK solvers. It will probably save you some time in implementation. RRT Connect is one option which is ...


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No, at every iteration your RRT* should give a more optimized path once it has found it. The fluctuations are strange. You should try to get a convergence similar to this one.


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Maybe there is a bit of misunderstanding about iterative methods for solving IK problems. Actually, an iterative IK solver does not necessarily require timestamps (or anything related to time). The general principle is that you start with some robot configuration (i.e. joint values) then you iteratively modify the configuration such that it eventually ...


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I asked this question on OMPL's mailing list. OMPL is an very popular motion planning library. Here is the response: https://sourceforge.net/p/ompl/mailman/message/35918890/ The answer is yes, they should be related.


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Dynamic Systems are described via system identification. That is a procedure to generate a physic engine on-the-fly. The physic engine can predict the future state of the system. An example: the quadrotor has a speed of 10 mph and runs into a wall. The physics engine aka "dynamic system" can predict the collison. RRT is used for solving the optimal control ...


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