Robotics (202-25161) - Spring 2002

Goals

Exercising material in chapters 1-5 of the Planning and Control book. This includes aspects of control and simulation, exercising TEMPLOG as a representation language, and planning. Also, improving soccer skills by better understanding of the pervading formal issues of the game. Think of this as one more step towards designing a robot soccer player, or umpire.

Requirements

1. You are asked to formalize several aspects of the soccer game. As a minimum, define axioms as follows:
   • Location and velocity of the ball (Newton's second law) For simplicity, ignore spin...
   • ``Off-side'', for a certain team.
   • A goal is scored in favor of a team.
2. Assume now that players can see omni-directionally and without error measure the POSITION of everything in the field. The STATE of the world is position, velocity, and acceleration of the ball and all players. Each player can decide to accelerate in any direction, and the accelerate commands work without error and with unlimited velocity or acceleration (unlike the simulator). Assume also that the players do NOT turn but again, can accelerate in any direction.
   • Is the world state as defined here completely observable?
   • Assuming only one agent on the field, that needs to get to the opposing goal within 10 seconds, with a final velocity of 1, with no opposition, is this problem controllable?
3. Write the following projection axioms:
   • If a player kicks a ball into the opposing goal from a distance of less than 10m, a goal will be scored for his team after a delay of less that 3 seconds.
   • If a player is holding the ball, and moves with it from location 1 to location 2, it will keep holding the ball and both will be at location 2 after the delay required to travel (assume constant velocity).
   • If a player moves without the ball to a certain location, it will get there after the required delay.
   • If a player grabs the ball, it will hold the ball if the player is in the same location as the ball.
4. Finally, we write the plan library and test whether it works.
   • Write a task decomposition axiom: to score a goal, you need to hold the ball, then move with it to near the goal, and then kick (move and kick are primitive).
   • Write task decomposition for holding the ball: be at ball location, then grab the ball (grab is primitive).
   • Write a task decomposition axiom for holding the ball: wait for a pass by a team member.
   • Show a task decomposition for the initial state, where the player is 50 meters from the goal, the ball is 40 meters from the goal (your choice as to exact location), and the task is to score a goal. Show temporal relations after decomposition to primitive actions.
   • Use the projection axioms to show that indeed a goal will be scored by the above plan and decomposition.

Deadline: Tuesday, April 30, 2002

Suggested Predicates to Use

It is heavily suggested that you use the following predicates (in addition to the standard predicates, such as equality, the ``holds'' relation, etc.). Otherwise, you will have to invent your own, which is MUCH harder... Use constants of your choice, such as for the team names, etc.