Study KKT dynamics against state constraints in OCP
It is possible that the two problems are equivalent. In such a case, it might be better to directly handle the contact constraint as a state constraint, either with penalty or aug-lag.
From KKT analyses, equality constraints (e.g. holonomic contact models) can be described as
- Laine Forrest and Claire Tomlin. Efficient Computation of Feedback Control for Constrained Systems
Another important paper to study that considers inequalities constraint is:
- Xie, Zhaoming et al. Differential dynamic programming with nonlinear constraints