Open Problems in Robotics
In the area of Motion Planning (my own area of research), the most that can be said is that <i>practical</i> solutions exist for a tiny subset of cases, <i>workable</i> methods exist for a larger subset, <i>expensive</i> methods exist for a still larger subset, and everthing else might as well be impossible.<p>- If you&#x27;ve got a low-dimensional problem, say 2D or 3D, without uncertainty (or at least bounded enough to pad obstacles and ignore it), search-based planners like A* and its derivatives <i>work</i>. Add uncertainty, complex non-holonomic constraints, limited horizons, etc and it becomes much harder.<p>- If you&#x27;ve got a higher dimensional problem, say a 6&#x2F;7-DoF arm, even multi-armed or humanoid robots, and you don&#x27;t have uncertainty and dynamics (or can ignore them), sampling-based planners like RRTs and PRMs and their derivatives will often practically work. Actually useful guarantees of finding a solution or trying to find an <i>optimal</i> solution in useful time are still very much unsolved.<p>- If your problem is basically open, and something approximating the &quot;straight-line&quot; from A to B is in the same local minima as a solution, trajectory optimization will work for a lot of problems. Motion planning is very much non-convex, though, so it&#x27;s very easy to go from a problem solvable with optimization to a problem that isn&#x27;t.<p>- Planning with non-rigid objects, significant uncertainty (effectively continuous MDPs or POMDPs), and&#x2F;or complex dynamics are all very unsolved problems.<p>For motion planning problems in the gray area of &quot;practically solvable&quot;, the art is figuring out how to simplify the problem as much as possible to make it tractable - highly optimized collision checking (generally speaking the performance bottelneck), combining search&#x2F;sampling-based + optimization methods to get an initial solution from a global method and then refining it towards a local minima with optimization, or using special hardware or sensors to bound dynamics and uncertainty so it can be ignored.