When traversing sharp corners, manufacturing machines are forced to tradeoff speed and accuracy. The most common way of reducing this tradeoff is to smooth the sharp corner using a pre-specified curve (e.g., a circular arc or spline). However, pre-specified curves cannot guarantee optimal performance. This paper presents a preliminary investigation into the potential of using methods from optimal control to minimize this tradeoff. First, a useful simplification is made to the exact cornering problem to make it tractable. Dynamic programming is then used to determine the best free-form curve that minimizes corner traversal time while adhering to path tolerance and machine kinematic constraints. Significant improvements in cornering time are demonstrated compared to two methods that use pre-specified curves. However, dynamic programming is found to be too computationally costly, thus impractical. Less computationally intensive techniques in optimal control are considered for future work.
