Inverse kinematics

About: Inverse kinematics is a research topic. Over the lifetime, 9215 publications have been published within this topic receiving 137731 citations. The topic is also known as: IK.

Backstepping Approach for Controlling a Quadrotor Using Lagrange Form Dynamics

Abstract: The dynamics of a quadrotor are a simplified form of helicopter dynamics that exhibit the same basic problems of underactuation, strong coupling, multi-input/multi-output design, and unknown nonlinearities. Control design for the quadrotor is more tractable yet reveals corresponding approaches for helicopter and UAV control design. In this paper, a backstepping approach is used for quadrotor controller design. In contrast to most other approaches, we apply backstepping on the Lagrangian form of the dynamics, not the state space form. This is complicated by the fact that the Lagrangian form for the position dynamics is bilinear in the controls. We confront this problem by using an inverse kinematics solution akin to that used in robotics. In addition, two neural nets are introduced to estimate the aerodynamic components, one for aerodynamic forces and one for aerodynamic moments. The result is a controller of intuitively appealing structure having an outer kinematics loop for position control and an inner dynamics loop for attitude control. The control approach described in this paper is robust since it explicitly deals with unmodeled state-dependent disturbances and forces without needing any prior knowledge of the same. A simulation study validates the results obtained in the paper.

Kinematic jump processes for monocular 3D human tracking

Abstract: A major difficulty for 3D (three-dimensional) human body tracking from monocular image sequences is the near nonobservability of kinematic degrees of freedom that generate motion in depth. For known link (body segment) lengths, the strict nonobservabilities reduce to twofold 'forwards/backwards flipping' ambiguities for each link. These imply 2/sup # links/ formal inverse kinematics solutions for the full model, and hence linked groups of O(2/sup # links/) local minima in the model-image matching cost function. Choosing the wrong minimum leads to rapid mistracking, so for reliable tracking, rapid methods of investigating alternative minima within a group are needed. Previous approaches to this have used generic search methods that do not exploit the specific problem structure. Here, we complement these by using simple kinematic reasoning to enumerate the tree of possible forwards/backwards flips, thus greatly speeding the search within each linked group of minima. Our methods can be used either deterministically, or within stochastic 'jump-diffusion' style search processes. We give experimental results on some challenging monocular human tracking sequences, showing how the new kinematic-flipping based sampling method improves and complements existing ones.

Kinematic control equations for simple manipulators

Abstract: The basis for all advanced manipulator control is a relationship between the cartesian coordinates of the end-effector and the manipulator joint coordinates. A direct method for assigning link coordinate systems and obtaining the end effector position, and Jacobian, in terms of joint coordinates is reviewed. Techniques for obtaining the solution to these equations for kinematically simple manipulators, which includes all commercially available manipulators, is presented. Finally the inverse Jacobian is developed from the solution.

An inverse kinematics architecture enforcing an arbitrary number of strict priority levels

Abstract: An efficient inverse kinematics solver is a key element in applications targeting the on-line or off-line postural control of complex articulated figures. In the present paper we progressively describe the strategic components of a very general and robust inverse kinematics architecture. We then present an efficient recursive algorithm enforcing an arbitrary number of strict priorities to arbitrate the fulfillment of conflicting constraints. Due to its local nature, the moderate cost of the solution allows this architecture to run within an interactive environment. The algorithm is illustrated on the postural control of complex articulated figures.

Modelling and Control of Robot Manipulators

Abstract: This book is the second edition of a textbook published in 1996 by McGraw Hill and originates from a graduate level course given by the authors at the University of Naples. The topics include kinematics, statics and dynamics of robot manipulators together with trajectory planning and active control. There are only minor additions the first edition, which are mainly the use of quaternion to describe the orientation of the end effector and a short description of a closed chain architecture for a manipulator (parallelogram arm). The book is largely devoted to serial manipulators, with special developments about active control including adaptative control, robust controls and stability analysis. Another strength of this book is the great number of problems proposed at the end of each chapter, together with a list of references related to it. The fundamental features covered by the text are illustrated on simple examples of serial manipulators (two-link planar arm, parallelogram arm) including analytical results and numerical tests. The book has nine chapters followed by three appendices. The first appendix is devoted to linear algebra, the second recalls some fundamental aspects of rigid body mechanics and the third gives some basic principles of feedback control of linear systems. Chapter one is an introduction to the study of robot manipulators, giving an interesting classification of their architectures, the corresponding workspace and describes the tasks for which they are used. After some standard examples of industrial manipulators, bibliographical reference texts are proposed, including textbooks on modelling and control of robots, general books on robotics, specialized texts, scientific robotic reviews and some international conferences on robotics. Chapters two, three and four are devoted to mechanical modelling of robot manipulators. The fundamental basics of kinematics are given in chapter two, including the representation of finite rotations by Euler angles or unit quaternions, homogeneous transformations, Denavit-Hartenberg parameters and workspace. The direct and inverse kinematical problems are solved in analytical form for some typical manipulator structures. The differential kinematics of robots are presented in chapter three, with an introduction to the geometric and analytic Jacobian matrices, kinematic singularities and redundancy. The inverse kinematic problem is presented, with special attention to the case of redundant robots where the solution is obtained by a linear optimization problem leading to the introduction of the pseudo-inverse Jacobian matrix and to the solution of several objectives such as avoidance of collision with an obstacle or moving away from singularities. Several inverse kinematics algorithms are given wih an interesting application to a three-link planar arm. Finally, a property of kineto-statics duality is deduced from the principle of virtual work applied to an equilibrium configuration of the robot. Chapter four is a standard presentation of the derivation of the dynamical model by Lagrange formulation and then by the Newton-Euler method. In the Lagrange formulation method, the linearity with respect to inertial parameters is shown and a detailed formulation of the dynamical model is obtained for a two-link Cartesian arm, a two-link planar arm and a parallelogram arm. The problem of dynamic parameter identification is also briefly presented from a numerical point of view. The recursive algorithm constructed from the Newton-Euler formulation is presented and illustrated by considering a two-link planar arm. Finally, the operational space dynamic model is introduced. In chapter five, paths and trajectory planning in joints and in operational spaces are presented; several classical methods of interpolation are described. Chapter six is an extensive study of active control of manipulators. Several methods are presented, involving classical independent joint control, non-linear centralized control, robust control and adaptative control. Both joint-space control and operational-space control are studied together with stability analysis by using Liapounoff functions. An interesting application to the two-link planar arm already used shows the comparison between various control schemes. Chapter seven deals with interaction control of serial manipulators with the working environment. Several strategies involving compliance control, impedance control, force control and hybrid control are presented. Chapter eight describes the actuators and the sensors used in robotics. Several types of servomotors (electric and hydraulic) are presented, together with the model giving their input/output relationship. Several kinds of sensors are also described including encoders, tachometers, force and vision sensors. The last chapter gives a short presentation of the functional architecture of a robot's control system, including characteristics of the programing environment and the hardware architecture. In conclusion, the book provides a good insight about simulation and control of robot manipulators, with a detailed study of the various control strategies and several interesting and pedagogical applications. This book is an excellent review of the standard knowledge needed not only for graduate students but also for researchers interested in robot manipulators. M Pascal