A program to control a robot manipulator for industrial assembly operations must take into account possible errors in parts placement and tolerances of the parts themselves. Previous approaches to this problem have been to (1) engineer the situation so that the errors are small or (2) let the programmer analyze the errors and take explicit account of them. This paper gives the mathematical underpinnings for building programs (plan checkers) to carry out approach (2) automatically. The plan checker uses a geometric CAD-type database to infer the effects of actions and the propagation of errors. It does this symbolically rather than numerically, so that computations can be reversed and desired resultant tolerances can be used to infer required initial tolerances or the necessity for sensing. The checker modifies plans to include sensing and adds constraints to the plan which ensure that it will succeed. An implemented system is described and results of its execution are presented. The plan checker could be used as part of an automatic planning system of as an aid to a human robot programmer.