Modeling and Design of Multirotors with Multi-joint Arms
This chapter presents the dynamic model of multirotors with multiple arms, which will be used for controller development in Part III and planning in Part V. It first presents the modeling of multirotors and arms individually, and them the coupled kinemati
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Abstract This chapter presents the dynamic model of multirotors with multiple arms, which will be used for controller development in Part III and planning in Part V. It first presents the modeling of multirotors and arms individually, and them the coupled kinematic and dynamic model of the aerial robot with multiple arms. The chapter also presents the methodology for designing a light robotic arm for aerial manipulation.
1 Introduction Aerial manipulators are complex multibody systems with coupled dynamic behavior which has to be taken in consideration in the design of each of their parts. This chapter presents the derivation of the dynamic model of a multirotor with multiple arms, which is important for controller development. It first presents the modeling of multirotors and arms individually, and then the coupled kinematic and dynamic model of the aerial robot with multiple arms. The analysis of the dynamic model shows that minimizing weight and mass distribution of the arms is very important for the stability and performance of the aerial manipulator. The chapter also presents the methodology for designing a light robotic arm for aerial manipulation.
G. Heredia (B) · A. Jimenez-Cano · A. Ollero GRVC Robotics Lab Sevilla, Universidad de Sevilla, Seville, Spain e-mail: [email protected] A. Jimenez-Cano e-mail: [email protected] A. Ollero e-mail: [email protected] R. Cano Civil Aerostructures Unit, Airbus Poland, Warsaw, Poland e-mail: [email protected] © Springer Nature Switzerland AG 2019 A. Ollero and B. Siciliano (eds.), Aerial Robotic Manipulation, Springer Tracts in Advanced Robotics 129, https://doi.org/10.1007/978-3-030-12945-3_2
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2 Modeling of Multirotors with Arms The dynamic behavior of an aerial manipulation system consisting of an aerial platform with one or more robotic arms is affected by variations in the mass distributions. This implies that the moments of inertia change significantly and the system center of mass moves continuously, introducing reaction forces and torques which compromise the stability of the aerial platform.
2.1 Modeling of Multirotors Consider a multirotor as the one shown in Fig. 1. Let F B be the coordinate frame attached to the center of mass of the vehicle’s body and FW be the inertial world-fixed coordinate frame in North-East-Down (NED) configuration, as shown in Fig. 1. The position of the aerial vehicle in the world reference frame, i.e. F B with respect to FW , is denoted by pb = [x y z]T , and its attitude is described by the yaw-pitchroll Euler Angles ηb = [ϕ θ ψ]T . The attitude of the UAV is defined by the following rotation matrix Rb ∈ S O(3), expressing the rotation of F B with respect to FW : ⎡
⎤ cθ cψ sφ sθ cψ − cφ sψ cφ sθ cψ + sφ sψ Rb = ⎣cθ sψ sφ sθ sψ + cφ cψ cφ sθ sψ − sφ cψ ⎦ −sθ sφ cθ cφ cθ
(1)
where s× and c× are abbreviations for sine and cosine, respectively. Moreover, let p˙ b describes the absolute linear velocity of the aerial vehicle, while ωb be its abso-
Fig. 1 An aerial manipulator with two robotic arms
Modeling
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