Efficient computation of inverse dynamics and feedback linearization for VSA-based robots

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 dynamicmodeling in symbolic form, does not use numerical approximations, grows linearly in complexity with the number of joints, and is suitable for online feedforward and real-time feedback control. A Matlab/C code is made available

Recursive Symbolic Calculation of the Dynamic Model of Flexible Parallel Robots

International audienceThis paper presents a symbolic and recursive calculation of the dynamic model of flexible parallel robots. In order to reduce the computational time, it is necessary to minimize the number of operators in the symbolic expression of the model. Some algorithms have been proposed for the rigid case, for parallel robots with lumped springs or for serial robots with distributed flexibilities, but to the best of our knowledge, nothing has been developed for parallel robots with distributed flexibilities. This paper aims at filling this gap. In order to minimize the number of operations, the Newton-Euler principle is used and combined with the principle of virtual powers. The Jacobian matrices defining the kinematic constraints are computed using recursive calculations that decrease the number of operators. The proposed algorithm is used to compute the elastodynamic model of a planar parallel robot. The obtained results, compared with those obtained with commercial softwares, show the validity of the proposed algorithm

Recursive and Symbolic Calculation of the Elastodynamic Model of Flexible Parallel Robots

International audienceThis paper presents a symbolic and recursive calculation of the elastodynamic model of flexible parallel robots. In order to reduce the computational time required for simulating the elastodynamic behavior of robots, it is necessary to minimize the number of operators in the symbolic expression of the model. Some algorithms have been proposed for the rigid case, for parallel robots with lumped springs or for serial robots with distributed flexibilities. In this paper, we extend the previous works to parallel robots with distributed flexibilities. The generalized Newton-Euler model is used and combined with the principle of virtual powers to minimize the number of operators and intermediate variables. Recursive calculations are proposed for the computation of the Jacobian matrices defining the kinematic constraints in order to decrease the number of operators. The proposed algorithm is used to compute the elastodynamic model of a prototype of a planar parallel robot developed at IRCCyN: the DualEMPS. The computed model is compared both with simulations done on Adams and with experiments. The validity of the approach in terms of result accuracy and computational time is demonstrated

Kinematic and dynamic analyses of general robots by applying the C-B notation-RaMIP (Robot and Mechanism Integrated Program)

In this thesis, a new symbolic representation based on 4x4 homogeneous matrices, C-B (Cylindrical Coordinates - Bryant Angles) notation, has been applied to the kinematic and dynamic analyses of general robots, and a computer algorithm named RaMIP (Robot and Mechanism Integrated Program) has been developed on a Sun workstation for the design and analysis of robots and mechanisms. RaMIP can be used to model most industrial robots currently in use. It performs three-dimensional kinematic and dynamic analyses and takes advantage of the computational efficiency of C-B notation. The C-B notation allows the user to model an arbitrary mechanism consisting of any combination of revolute, prismatic and spherical joints. RaMIP has the capability of presenting results in the form of two- and three-dimensional plots of colored contours, as well as tables of numerical data. The algorithm is examined and tested by analyzing several commercial robots. Kinematic and dynamic results are computed and presented in two- and three-dimensional graphs and compared with known data to probe the validity and accuracy of RaMIP. It should be noticed that the efforts completed in this thesis present only the first step towards the implementation of a general purpose computer algorithm -RaMIP- for the automated design and analysis of open- and closed-chain mechanisms utilizing C-B notation

A hybrid dynamic model for bio-inspired soft robots - Application to a flapping-wing micro air vehicle.

International audienceThe paper deals with the dynamic modeling of bio-inspired robots with soft appendages such as flying insect-like or swimming fish-like robots. In order to model such soft systems, we propose to use the Mobile Multibody System framework introduced in [1][2][3]. In such a framework, the robot is considered as a tree-like structure of rigid bodies where the evolution of the position of the joints is governed by stress-strain laws or control torques. Based on the Newton-Euler formulation of these systems, we propose a new algorithm able to compute at each step of a time loop both the net and passive joint accelerations along with the control torques supplied by the motors. To illustrate, based on previous work [4], the proposed algorithm is applied to the simulation of the hovering flight of a soft flapping-wing insect-like robot (see the attached video)

Improved Lighthill fish swimming model for bio-inspired robots - Modelling, computational aspects and experimental comparisons.

International audienceThe best known analytical model of swimming was originally developed by Lighthill and is known as large amplitude elongated body theory (LAEBT). Recently, this theory has been improved and adapted to robotics through a series of studies [Boyer et al., 2008, 2010; Candelier et al., 2011] ranging from hydrodynamic modelling to mobile multibody system dynamics. This article marks a further step towards the Lighthill theory. The LAEBT is ap- plied to one of the best bio-inspired swimming robots yet built: the AmphiBot III, a modular anguilliform swimming robot. To that end, we apply a Newton-Euler modelling approach and focus our attention on the model of hydrodynamic forces. This model is numerically in- tegrated in real time by using an extension of the Newton-Euler recursive forward dynamics algorithm for manipulators to a robot without a fixed base. Simulations and experiments are compared on undulatory gaits and turning manoeuvres for a wide range of parameters. The discrepancies between modelling and reality do not exceed 16% for the swimming speed, while requiring only the one-time calibration of a few hydrodynamic parameters. Since the model can be numerically integrated in real time, it has significantly superior accuracy com- pared with computational speed ratio, and is, to the best of our knowledge, one of the most accurate models that can be used in real-time. It should provide an interesting tool for the design and control of swimming robots. The approach is presented in a self contained manner, with the concern to help the reader not familiar with fluid dynamics to get insight both into the physics of swimming and the mathematical tools that can help its modelling

An efficient finite element formulation of dynamics for a flexible robot with different type of joints

If two adjacent links of a flexible robot are connected via a revolute joint or a fixed prismatic joint, the relative motion of the next link will depend on both the joint motion and the elastic displacement of the distal end of the previous link. However, if the two adjacent links are connected via a sliding prismatic joint, the relative motion of the next link will depend additionally on the elastic deformation distributed along the previous link. Therefore, formulation of the motion equations for a multi-link flexible robot consisting of the revolute joints, the fixed prismatic joints and the sliding prismatic joints is challenging. In this study, the finite element kinematic and dynamic formulation was successfully developed and validated for the flexible robot, in which a transformation matrix is proposed to describe the kinematics of both the joint motion and the link deformation. Additionally, a new recursive formulation of the dynamic equations is introduced. As compared with the previous methods, the time complexity of the formulation is reduced by O(2η), where η is the number of finite elements on all links. The numerical examples and experiments were implemented to validate the proposed kinematic and dynamic modelling method

Modelling and Simulation of a Two wheeled vehicle with suspensions by using Robotic Formalism

International audienceModels, simulators and control strategies are required tools for the conception of secure and comfortable vehicles. The aim of this paper is to present an efficient way to develop models for dynamic vehicle, focusing on a two wheeled vehicles whose body involves six degrees of freedom. The resulting model is sufficiently generic to perform simulation of realistic cornering and accelerating behavior in various situations. It may be used in the context of motorcycle modeling, but also in various situations (e.g. for control application) as simplified model for 3 or 4 wheeled (tilting) cars. The approach is based on considering the vehicle as a multi-body poly-articulated system and the modeling is carried out using the robotics formalism based on the modified Denavit-Hartenberg geometric description. In that way, the dynamic model is easy to implement and the system can be used for control applications

Kinematically optimal hyper-redundant manipulator configurations

“Hyper-redundant” robots have a very large or infinite degree of kinematic redundancy. This paper develops new methods for determining “optimal” hyper-redundant manipulator configurations based on a continuum formulation of kinematics. This formulation uses a backbone curve model to capture the robot's essential macroscopic geometric features. The calculus of variations is used to develop differential equations, whose solution is the optimal backbone curve shape. We show that this approach is computationally efficient on a single processor, and generates solutions in O(1) time for an N degree-of-freedom manipulator when implemented in parallel on O(N) processors. For this reason, it is better suited to hyper-redundant robots than other redundancy resolution methods. Furthermore, this approach is useful for many hyper-redundant mechanical morphologies which are not handled by known methods