Direct collocation (DC) is a widely used method for solving dynamic optimization problems (DOPs), but its implementation simplicity and computational efficiency are limited for challenging problems. For DOPs involving singular arcs, DC solutions often exhibit significant fluctuations along the singular arc, accompanied by
large residual errors between collocation points, where the
dynamic constraints are enforced as equality constraints.
In this paper, we introduce the direct transcription method
of integrated residual regularized direct collocation (IRRDC). This approach enforces dynamic constraints using a combination of point-wise residual constraints (expressed
as either equalities or inequalities) and a penalty term on
the integrated residual error, which helps reduce errors between collocation points. IRRDC retains the implementation simplicity of DC while improving both solution accuracy and efficiency, particularly for challenging problem types. Through the examples, we demonstrate that for problems where traditional DC results in excessive fluctuations, IR RDC effectively suppresses fluctuations and yields solutions with greater accuracy — at least two orders of magnitude lower in various error measures in relation to the dynamic and path constraints.