We introduce Pinocchio, an open-source software framework that implements rigid body dynamics algorithms and their analytical derivatives. Pinocchio does not only include standard algorithms employed in robotics (e.g., forward and inverse dynamics) but provides additional features essential for the control, the planning and the simulation of robots. In this paper, we describe these features and detail the programming patterns and design which make Pinocchio efficient. We evaluate the performances against RBDL, another framework with broad dissemination inside the robotics community. We also demonstrate how the source code generation embedded in Pinocchio outperforms other approaches of state of the art.

We develop a recursive numerical algorithm to compute the inverse dynamics of robot manipulators with an arbitrary number of joints, driven by Variable Stiffness Actuation (VSA) of the antagonistic type. The algorithm is based on Newton-Euler dynamic equations, generalized up to the fourth differential order to account for the compliant transmissions, combined with the decentralized nonlinear dynamics of the variable stiffness actuators at each joint. A variant of the algorithm can be used also for implementing a feedback linearization control law for the accurate tracking of desired link and stiffness trajectories. As in its simpler versions, the algorithm does not require dynamic modeling in symbolic form, does not use numerical approximations, grows linearly in complexity with the number of joints, and is suitable for on-line feedforward and real-time feedback control. A Matlab/C code is made available.

We present a control methodology for underactuated aerial manipulators that is both easy to implement on real systems and able to achieve highly dynamic behaviors. The method is composed by two parts, a nominal input/state generator that takes into account the full-body nonlinear and coupled dynamics of the system, and a decentralized feedback controller acting on the actuated degrees of freedom that confers the needed robustness to the closed-loop system. We show how to apply the method to Protocentric Aerial Manipulators (PAM) by first using their differential flatness property on the vertical 2D plane in order to generate dynamical input/state trajectories, then statically extending the 2D structure to the 3D, and finally closing the loop with a decentralized controller having the dual task of both ensuring the preservation of the proper static 3D immersion and tracking the dynamic trajectory on the vertical plane. We demonstrate that the proposed controller is able to precisely track dynamic trajectories when implemented on a standard hardware composed by a quadrotor and a robotic arm with servo-controlled joints (even if no torque control is available). Comparative experiments clearly show the benefit of using the nominal input/state generator, and also the fact that the use of just static gravity compensation might surprisingly perform worse, in dynamic maneuvers, than the case of no compensation at all. We complement the experiments with additional realistic simulations testing the applicability of the proposed method to slightly non-protocentric aerial manipulators.

We consider the problem of computing the inverse dynamics of a serial robot manipulator with N elastic joints in a recursive numerical way. The solution algorithm is a generalized version of the standard Newton-Euler approach, running still with linear complexity O(N) but requiring to set up recursions that involve higher order derivatives of motion and force variables. Mimicking the case of rigid robots, we use this algorithm and a numerical factorization of the link inertia matrix (which needs to be inverted in the elastic joint case) for implementing on-line a feedback linearization control law for trajectory tracking purposes. The complete method has a complexity that grows as O(N^3). The developed tools are generic, easy to use, and do not require symbolic Lagrangian modeling and customization, thus being of particular interest when the number N of elastic joints becomes large