## 5 Safe and Accurate Aerial Manipulation
### Planning Methods for Aerial Manipulation  
Devices such as bird diverters have to be installed every 5-10 m. Since the length of each segment of a power line is typically above 150 m, this implies the installation of a large number of devices. Moreover, taking into account the limited payload capacity of the aerial platform, it is expected that the aerial robot has to move frequently to a supply point where the devices are stored. Consequently, it is proposed the application of planning methods that generate the most efficient trajectories in terms of energy consumption for the aerial manipulator in order to maximize the number of installed devices. To the best of the authors' knowledge, this paper proposes for the first time the use of planning methods for the efficient installation of devices on power lines.  
Power lines are linear structures that admit a graph-based representation, where the nodes model the electric towers and the edges model the segments of the power line. These power lines are usually located in open environments with sparse obstacles, such as trees or buildings, but where weather factors, especially wind, play an important role when operating with aerial robots. Taking into account the features above, the planning problem is suitable to be addressed as a vehicle routing problem in which the obstacles are neglected. Later, during the robot operation, these obstacles can be avoided using a collision-avoidance system working at a local level.  
Focusing on the formulation of the vehicle routing problem for the aerial manipulation platforms described in Section 4.1, the general approach proposed in this paper is based on covering all the segments of the power line while minimizing the energy consumption. For this, simplified but realistic models of energy consumption are required to define edge costs. These models should consider the hybrid locomotion capabilities of some of the presented aerial manipulators. Therefore, the graph representation of the power line is composed  
Figure 9: Error signals for the controlled states of the passively tilted hexarotor.  
of two kinds of edges. Firstly, rolling edges are associated with the power line. Secondly, flying edges are associated with either aerial transitions between segments/points of the power line or connections of the power line with the supply point. Moreover, the consideration of effects, such as the wind, transforms the graph into a directed one since its edges have asymmetric costs. Finally, constraints such as the maximum robot payload or the battery capacity allow closing the definition of the problem.  
Figure 10 shows some preliminary planning results for the installation of clip-type bird diverters on the represented power line, using both MLMP and the DM-C platforms. The problem was solved using linear programming after imposing the following requirements: (a) all the power lines should be covered rolling once, (b) minimizing the total energy consumption, (c) taking into account the maximum robot payload (10 devices for the MLMP and no limits for the DM-C because the aerial platform provides the devices), and (d) visiting the supply point to load the devices when it is needed. The number of diverters to be installed in each segment of the power line is indicated inside the circles in the figure. For these results, no wind was considered and the cost of rolling per unit of distance was fixed to be lower than the cost of flying. As can be seen in the figure, the proposed planning method computes efficient routes that are compatible with the imposed constraints.