We aim to solve the problem of path following for kinematically redundant manipulators over SE(3). Trajectory optimization (TO) is a solution to generate a joint-space trajectory while satisfying physical constraints along with the path-following objective. Unfortunately, as many constraints are imposed over the objective, the optimization is prone to fall into local minima and requires time-consuming re-starts. To ameliorate this problem, we propose a learning-based initial-trajectory generation method that returns joint-space trajectories as good initial guesses for TO. Our method learns the kinematically feasible null-space motions following a target path over a multi-task reinforcement learning framework with demonstration guidance. We evaluate the proposed method and three baseline initial trajectory generation methods plugged into two representative TO frameworks. We show that our method boosts the performance of the optimization methods in terms of optimality, computational efficiency, and robustness.
Finally, we verify the optimized trajectory quality using our initialization method by executing it on a real Fetch robot and show a better accurate and smooth tracking performance.