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6. Suppose that you have a robot capable of performing two tasks in manipulating blocks on a large tabletop: . PLACE BLOCK X ON BLOCK Y: This action places the block x on top of the block y. Preconditions for applying this action are that both block x and block y have clear tops (so there is no block on top of x ory). The robot will automatically locate the specified blocks. . CLEAR BLOCK X: This action removes any block from the top of block x. A necessary precondition for this action is that block x has one and only one block on top. The block removed is placed on the table top. For this robot, answer the following questions: 1. Using only the two robot actions, specify a sequence of robot actions to take the five blocks shown in Figure 9-10(a) to the position shown in Figure 9-10(b) in five or six robot actions. 2. Specify a sequence of robot actions to move the blocks from position (b) to position (c) in Figure 9-10 in six moves. 3. Develop an activity network for the robot actions in moving from position (b) to position (c) in Figure 9-10. Prepare both activity-on-node and activity-on-link representations. Are there alternative sequences of activities that the robot might perform to accomplish the desired position? D C A E A C B B D B D E E A C (a) (b) (c) Figure 9-10 Illustrative Block Positions for Robot Motion Planning 7. In the previous problem, suppose that switching from the PLACE BLOCK action to the CLEAR BLOCK action or vice versa requires an extra ten seconds. Movements themselves require 8 seconds. What is the sequence of actions of shortest duration to go from position (a) to position (c) in Figure 9-10