Is the problem statement challenging enough to be completed in 8
It is hard to tell. In this project, you are tackling several problems at once. All of them requires a solid and at least an advanced-intermediate level of knowledge in physics, math, programming and robotics. For real-case scenario, probably the problems are less in comparison with simulation because you don't need to handle modeling the system. What I would say is 8 weeks are enough but you need extra work than 5 hours (i.e. may be 10). For your case, what I would suggest is to do the following:
1- (Half Week) Finish modeling the system (i.e. requires physics knowledge and half week for this problem is enough). Use Newton's or Lagrangian's approaches. Come up with the differential equations that govern the motion of the system. For saving time, you may consider reading some articles that already done this work with this robot.
2- (Half Week) Finish solving the differential equations (i.e. requires math and in particular numerical method knowledge and programming, matlab will do the hard work for you). Put the ODEs equations in a compact form.
3- (One Week) Choose control approach to move your robot from one point to another. In your case, I will carry out the PD-computed torque controller. It is simple and efficient if you don't have uncertainty in the system, if you do then choose PID-computed torque approach. Perform several tests to make sure that the robot is ready to follow the trajectory efficiently with a reasonable speed. At this stage your robot can move and follow any trajectory BUT it doesn't react with the environment.
4- (Two Weeks) Be acquainted with how the robot interacts with the environment in order to pick up objects (i.e. requires some robotics knowledge). Also, you need to understand how to get data from sensors and let the robot decide for a proper action. For example, when the robot should pick up an object? How does robot know?
5- (Two Weeks) understand obstacles avoidance approaches (i.e. requires some robotics knowledge). Pick up the simplest approach since you don't have an ample time to handle different approaches.