In this paper we propose an energy efficient method for path planning by a robot arm. First we have developed a cost function that provides a set of via points determining a suitable path according to the obstacles present in the surroundings and other restrictions in its motion. Then we fit a suitable polynomial to this set of interior points to ensure that the journey is smooth and takes place with the consumption of minimum energy. The set of via-points as well as the minimum energy path have been determined using IWO (Invasive Weed Optimization) which is a new search heuristic based on the colonizing property of weeds. Application of such evolutionary algorithms in trajectory planning is advantageous because the exact solution to the path planning problem is not always available beforehand and must be determined dynamically. The entire procedure has been demonstrated through simulations. The above formulation is very simple and versatile and can be effectively applied to a variety of situations.