This topic always reminds me of my most embarrassing programming/math failure. Many years ago, Minsky invented a robotic arm design, and master machinist Bill Bennett made it. (Google “Minsky Bennett arm”.) It had 8 hinge joints, so it would seem that deploying the “hand” end to any given position and orientation (6 space) would be easy, due to the 2 degrees of freedom. I was asked to write a program to move the arm to any desired goal. The only approach I knew was hill climbing. The computation of end position and orientation from the flexion of the 8 joints was straightforward. But the hill climber kept getting stuck close to the goal, in local minima. I tried perturbations in the neighborhood. I tried using the derivatives of two joints moving simultaneously. Maybe also three or more simultaneously, I don’t remember. I gave it goals that result from roughly midrange positions of the joints, so I knew the goals were achievable and not along some boundary plane of joint space. All to no avail. It often got stuck in local minima, close but too far for a robot hand to reasonably do something like pick up a block. I had to give up. I don’t think anyone else tried to write a deployer. My failure resulted in the arm, a wonder of engineering and very organic looking, being relegated to curiosity status. Last I knew, it was on display at the MIT museum. — Mike
On Feb 17, 2016, at 10:01 AM, James Propp <jamespropp@gmail.com> wrote:
Does anyone have a favorite example of a fake optimum?