## 1 Introduction  
AErial RObotic Manipulators (AEROMs) [1, 2] are combined systems, composed of mobile platforms and robotic manipulators. The mobile platform system is usually a UAV, while the robotic manipulator system includes one or several arms. The increasing demands of aerial pipeline maintenance, bridge inspection, fruit picking, etc. call for application of aerial robotic manipulators to perform tasks in aerial environment. Examples include \"Aerial Cognitive Integrated Multi-task Robotic System with Extended Operation Range and Safety\" [3], \"Aerial Robotic Training for the Next Generation of European Infrastructure and Asset Maintenance Technologies\" [4], \"Hybrid Flying-rollIng with Snake-arm Robot for Contact Inspection\" [5] and \"Aerial Robotic System Integrating Multiple Arms\" [6]. In these programs, aerial missions are performed with various categories of aerial robotic manipulators, as shown in Figure 1. In Figure 1a-c, the robotic manipulator locates on the top of UAV base, opposite to Figure 1d-f. A category of combined system is of great interest to both scientists and practitioners. As shown in Figure 1a,d, the system consists of a UAV and a single-arm robotic manipulator. This is because the modelling is with lower difficulty and the system is easily controlled. However, the combined system still exhibits some special characteristics. Strong coupling exists between the robotic manipulator and the UAV. Moreover, the manipulator is dynamically singular. Accordingly, specific trajectory planning strategies have to be investigated to cope with the aforementioned problems. The developments of an AEROM system includes structure design, mathematical modelling, trajectory planning, control, etc. Actually, an AEROM model includes two parts, the kinematic model and the dynamic model. The trajectory planning is studied on the basis of AEROM kinematics [7, 8], while the control development is based on both kinematics and dynamics [9]. The trajectory planning aims at optimizing joint trajectories, end-effector trajectories or UAV trajectories. As a matter of fact, the trajectory planning has been well developed for robots in outer space [7, 8], where the satellite base is usually under free-floating mode. Two common trajectory planning techniques are respectively based on inverse kinematics and forward kinematics. For the technique using inverse kinematics, various concepts have been proposed, including Generalized Jacobian Matrix [9], Enhanced Disturbance Map [10], Path Dependent/Independent workspace [11] and Reaction Null Space [12]. However, this approach can result in singularities. This shortage is well avoided in the technique using forward kinematics, where the trajectory planning issue is transformed into an optimization issue. Intelligent Optimization Algorithms (IOAs) are utilized to solve the optimization issue. The procedure based on forward kinematics is followed. In order to perform optimization, joint trajectories are firstly parametrized with mathematical functions such as sinusoidal functions [13, 14], polynomial functions [15, 16], spline functions [17, 18], etc. Second, a few function coefficients are evaluated according to initial conditions, including joint angles, joint velocities, joint accelerations or EE pose at initial time or final time. Third, values of unknown function coefficients are searched via IOAs, in conjunction with fitness functions and constraint conditions. Common IOAs include evolutionary algorithms like GA [19, 20] and Differential Evolution (DE) algorithm [21, 22], swarm intelligence algorithms like PSO [23, 24] and Ant Colony Optimization [25, 26], Neural Network Algorithm [27, 28], etc. Fitness functions are usually minimum path length, time spent or energy cost. Constraint conditions denote limits on joint angles, joint velocities and joint accelerations. This paper proposes a novel approach for trajectory planning of an aerial robotic manipulator, coping with multiple constraints and objectives.