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    <p>This is a reasonably challenging problem, and it's not likely that you'll find a good solution with <em>ad hoc</em> control rules. In the robotics literature, the problem is expressed as a target-tracking one (Google "target tracking robot motion planning" for some interesting reading.)</p> <p>I've implemented target-tracking for a ground-based, wheeled robot, and I think the methods would apply to your problem. Furthermore, I think they will scale well to the added 3rd dimension of motion in your problem. Take a look at implementing "potential fields". This method models the robot, targets, and/or obstacles as particles with electric charges. Targets exhibit attractive forces; obstacles are modeled with repulsive forces. This model is easy to implement and works surprisingly well for simple tracking / avoidance tasks.</p> <p><a href="http://www.cs.utexas.edu/~pstone/Courses/395Tfall05/resources/week9b-ben-potential-fields.ppt" rel="nofollow">Here</a> is a set of slides that introduces the topic. <a href="http://users.isr.ist.utl.pt/~mir/pub/ObstacleAvoidance.pdf" rel="nofollow">Here</a> is a pretty good paper on using potential fields for obstacle avoidance. It shouldn't be much of a task to apply those methods to a tracking problem (just invert the signs!). Last, <a href="http://dl.acm.org/citation.cfm?id=1465439" rel="nofollow">here</a> is a an ACM paper in which the author describe solving a similar target-tracking problem. (I don't have access to the PDF, sorry).</p>
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