**1. Introduction**

A change in task-specification is often unavoidable in real-world manipulation problems. For example, consider a scenario where a manipulator is handing over an object to a human. The robot's estimate of the goal position can change as it executes its prior computed trajectories. Consequently, it needs to quickly adapt its joint motions to reach the new goal position. In this paper, we model motion planning as a parametric optimization problem wherein the task specifications are encoded in the parameters. In this context, adaptation to a new task requires re-computing the optimal joint trajectories for the new set of parameters. This is a computationally challenging process as the underlying cost functions in typical manipulation tasks are highly non-linear and non-convex [1]. Existing works leverage the so-called warm-starting technique where prior computed trajectories are used as initialization for the optimization solvers [2]. However, our extensive experimentation with off-the-shelf optimization solvers such as Scipy-SLSQP [3] show it is not sufficient for real-time adaptation of joint trajectories to task perturbations.
