As technology advances, the barriers between the co-existence of humans and robots are slowly coming down. The prominence of physical interactions for collaboration and cooperation between humans and robots will be an undeniable fact. Rather than exhibiting simple reactive behaviors to human interactions, it is desirable to endow robots with augmented capabilities of exploiting human interactions for successful task completion. Towards that goal, in this paper, we propose a trajectory advancement approach in which we mathematically derive the conditions that facilitate advancing along a reference trajectory by leveraging assistance from helpful interaction wrench present during human-robot collaboration. We validate our approach through experiments conducted with the iCub humanoid robot both in simulation and on the real robot.