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Concept# Inverse dynamics

Résumé

Inverse dynamics is an inverse problem. It commonly refers to either inverse rigid body dynamics or inverse structural dynamics. Inverse rigid-body dynamics is a method for computing forces and/or moments of force (torques) based on the kinematics (motion) of a body and the body's inertial properties (mass and moment of inertia). Typically it uses link-segment models to represent the mechanical behaviour of interconnected segments, such as the limbs of humans or animals or the joint extensions of robots, where given the kinematics of the various parts, inverse dynamics derives the minimum forces and moments responsible for the individual movements. In practice, inverse dynamics computes these internal moments and forces from measurements of the motion of limbs and external forces such as ground reaction forces, under a special set of assumptions.
Applications
The fields of robotics and biomechanics constitute the major application areas for inverse dynamics.
Within robotics,

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A global approach to the problem of model-based control of fast parallel robots is proposed in this work. Fundamental differences between the well-known serial arms and parallel manipulators are first explained. A formalism inspired from Denavit-Hartenberg's makes it possible to parametrize any parallel manipulator by handling it as two tree robots connected through six standard links. Then, it is shown that kinematics and dynamics modeling is greatly simplified when the robot's state is represented both by the variables associated to the actuated joints and the variables specifying the end-effector's position in operational space. The inverse dynamics model of any parallel manipulator can then be put under a standard form called "in the two spaces". A Newton-Euler based algorithm is proposed for the real-time computation of the model in the two spaces its complexity is shown not to be much larger than for serial arms. Through Lagrangian mechanics, the model in the two spaces allows analysis of the robot's dynamics properties, such as passivity. These properties are shown to be equivalent to those of serial arms, except that parallel robots offer good performances only in a restricted workspace in which their Jacobian matrix remains bounded. Various control strategies for the trajectory tracking problem for fast robots are then examined. The advantages of model-based approaches combined with robust feedback laws in operational space are described. It is shown that a control loop in operational space requires less computations than in joint space for a parallel robot. Moreover, such a scheme can be very efficiently be implemented on a multiprocessor control unit that exploits the intrinsically parallel and pipeline structure of the required algorithms. Finally, the proposed approach is applied to the Delta parallel manipulator. A systematic approach leads to the kinematics and dynamics models of this robot, which are expressed under a very compact form. The analysis of the Delta's Jacobian matrix as well as some simulation results reveal the advantages and weak points of this manipulator. The implementation of a model-based control law for the Delta on a control unit with four Transputers is described. Some results obtained on a Delta with a crank belt reduction are presented and discussed.

The shoulder complex is a complex articulation of the human body. It consists of several bones and joints and is moved and stabilized by 16 muscles. The muscle forces can not be measured experimentally, but can be computed using numerical methods. An existing numerical model of the shoulder uses inverse dynamics and nullspace optimization to compute these forces. The muscle segments in the model are modelled as cables that wrap around the underlying bony structure. The project’s aim is to adapt the existing model and introduce the parametrization of the number of cables. Therefore, origin and insertion areas were interpolated with curves and the muscle cables were evenly distributed on these curves. The results showed that at least three cables per muscle segment needs to be used, to get consistent results. The present work demonstrates thus, that the number of cables per muscle segment plays an important role. The necessary number of cables should always be investigated whenever muscles are simplified by cables.

2014, , ,

The inverse dynamics of a robotic manipulator is instrumental in precise robot control and manipulation. However, acquiring such a model is challenging, not only due to unmodelled non-linearities such as joint friction, but also from a machine learning perspective (e.g., input space dimension, amount of data needed). The accuracy of such models, regardless of the learning techniques, relies on proper excitation and exploration of the robot's configuration space, in order to collect a rich dataset. This study aims to provide rich data in learning the inverse dynamics of a serial robotic manipulator using supervised machine learning techniques. We propose a method, called Max-Information Configuration Exploration (MICE), to incrementally explore and generate information-rich data via computing parameters of a trajectory set. We also introduce a new set of excitation trajectories that explores robot's configuration through imposed stable limit cycles in robot joints' phase space while satisfying feasibility constraints and physical bounds. We benchmark MICE against state-of-the-art in terms of data quality and learning accuracy. The proposed methodology for data collection, model learning, and evaluation, is validated with a KUKA IIWA14 robotic arm where the results prove significant improvement over traditional approaches.