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Having very little experience in construction, we set out to make a simple, yet effective robot design.
The robot is driven by two large wheels, each powered by a motor (geared down through a gearbox). There aren't any other wheels touching the ground. Two smooth lego pieces are on the front for the robot to rest on in place of a third wheel. The battery pack, the heaviest component on the robot by far, is towards the front to make sure the robot works great.
The main attraction is the rod-claw that is very prominently attached to the robot. (See the pics.) A servo lifts this arm up and down. When this claw is at the down position, the spacing of the rods is such that it is able to slide under a big ball but can still lift the big ball up when the instruction comes to lift up the arm. The arm lifts halfway between the down and up position as the robot backs into the scoring area, after which the arm lifts all the way up and slam dunks the ball into the scoring area. A ramp attached on the top of the robot helps guide the ball in.
In addition to this claw, there is a very simple bulldozer on the reverse side of the robot that can push balls in straight lines. This is synergetic with the claw because as the robot backs into the scoring area pushing one or two small balls in, it will be well-positioned to dump a big ball into the goal as well.
The robot finds its starting orientation by way of two distance sensors, one on the front and one on the left. Although the distance sensors are not accurate at these kinds of ranges, the reading for a close wall is still different enough from a reading from a far wall that they are easily used.
In addition, there are two bump sensors at the rear of the robot. These are very important. Telling a robot to drive x centimeters is very error prone, but telling a robot to back up until it is flush with a wall (both bump sensors are pressed) is quite accurate, at least in one direction. Backing up to a pair of perpendicular walls is a great way to set your position accurately. (i.e. back up to the short wall, go forward x cm. Turn, Back up to the long wall, go forward y cm, to get to the point (x,y))