Robot Arm Matrix Answer Which of the following values should it be? Plus 1, minus 1, or zero? OK, good. The correct answer is minus 1. Now let's look at the top row. The top row is meant to give us the first derivative, delta x. So we will have delta L plus one delta L minus one delta theta. Therefore, our top row is made up of plus one delta L minus one delta theta. And similarly, for the bottom row, we want delta y to be 0 delta x plus one delta θ. So we have 0 delta L plus one delta θ. So that's our matrix. This matrix converts between delta L and delta theta. We changed the controller and delta x delta y, which is the change in how the robot actually moved. Let's look at a few examples to see how this works. First, let's copy that. 1 minus 1 times delta l delta theta equals delta x delta y. Now we can play around with different values for delta l and delta theta. Thus, the one in the picture there is 1 minus 1 0 1. The delta l is 0.1 and the delta theta is -0.1. We performed this task in the picture. To perform this task, I moved to a location on the controller corresponding to 0.1, and then moved a second time to a location corresponding to 0.1. 0.1 plus another 0.1, so 0.2, 0 minus 0.1. If I had made those two movements, then the robot would have moved 0.1 units in the negative direction. I used this technique to draw the arrow on the controller. If I do this, the tip of the finger moves in that direction. Let's sanity check this without doing the math. What did I tell the robot to doI told the robot to increase "l" by 0.1, decrease "theta" by 0.1, and then repeat this process indefinitely. The robot therefore increases "l", then decreases "theta", then repeats this process indefinitely. OK so it does that.