For a given motion task, an ideal Optimal Control (OC) solver could plan the entire future motion trajectory of arobot in real-time. However, this ideal scenario cannot bereached because of a few factores. (i) These OC problems are typically highly non-convex. (ii) Motion of a robot (typically legged robots) often requires interaction with the environment (contacts and contact forces). These constraints are difficult to solve. (iii)The computation time increases exponentially with theDoF(Degrees of Freedom) of the robot, and the lengthof future (horizon) being planned.In this short presentation, summarizing our presentation, we will recap our recent effortstowards approximating the above stated ideal scenario. Ourpresentation consists of four works, which all bind towardsthe same goal.