We present a reformulation of the posture generation problem that encompasses non-Euclidean manifolds. Such a formulation allows a more elegant mathematical description of the constraints, which we exemplify through some scenarios in the simulation results section. In our previous work, the posture generation problem is formulated as a non-linear optimization program with constraints expressed only through Euclidean manifolds; we solve the latter problem using on-the-shelf solvers. Instead, we decided to implement a new SQP solver that is most suited to non-Euclidean manifolds structural objects. By doing so, we have a better mastering in the way to tune and specialize our SQP solver for robotic problems.