www.dotproject.com is an a link to an open source project management tool. It will allow you to enter tasks and task dependencies. It also generates Gantt charts.
Part of project management that would be beneficial to address is risk management. For each requirement or set of dependent tasks, maintain a risk list and try to mitigate them. High risk tasks should be pushed earlier in the schedule.
A task like "produce drive module code" has very clear risks:
1) If the task is not completed before the drive train is completed you will hold up testing of the rest of the robot and driver training.
2) If the task is not complete before ship date you can't compete.
The mitigation is easy:
1) Incrementally code/test/verify starting with the most basic code needed to move. Once that's working then add bells and whistles to fill out the schedule.