Real-Time Inverse Kinematics Techniques for Anthropomorphic Limbs

Abstract

In this paper we develop a set of inverse kinematics algorithms suitable for an anthropomorphic arm or leg. We use a combination of analytical and numerical methods to solve generalized inverse kinematics problems including position, orientation, and aiming constraints. Our combination of analytical and numerical methods results in faster and more reliable algorithms than conventional inverse Jacobian and optimization-based techniques. Additionally, unlike conventional numerical algorithms, our methods allow the user to interactively explore all possible solutions using an intuitive set of parameters that define the redundancy of the system.

Presenting in Virtual Worlds: Towards an Architecture for a 3D Presenter Explaining 2D-Presented Information

“…If the pointing target's location and size determine the wrist position, we can analytically calculate elbow and shoulder joint rotations using the inverse-kinematics strategy that Deepak Tolani, Ambarish Goswami, and Norman Badler describe. 13 The elbow, though, is still free to swivel on a circular arc, whose normal is parallel to the axis from the shoulder to the wrist. To create reasonably good-looking movements, the presenter always rotates the elbow downward.…”

Evolutionary motion inverse kinematics

“…The goal is to minimise the distance between the end-effector and goal position simple manipulators with a fixed number of joints and some special cases there are efficient closed form solutions to IK. However, for the general case there does not exist an analytic solution to IK [5]. Manipulators with more than one joint are said to be redundant as there may exist a variable number of possible solutions that may be discrete or infinite depending on the circumstances.…”

“…Kinematic decoupling can be used to break a complicated articulated structure into several simple ones that can be solved analytically [5]. Analytic solutions are fast and yield all possible solutions for a given end-effector position.…”

“…Numerical solutions to IK can be characterised as starting with an initial guess and iteratively converging towards a single solution [5]. Numerical methods can be used on any type of kinematic structure, although performance may vary depending on the technique used.…”

“…The problem is treated as finding the roots of a series of nonlinear equations representing the difference between the end-effector and goal position given a series of joint variables. Since only first-order approximations are used this method can be slow to converge at an optimal solution and may encounter problems with singularities preventing a solution from being found [5]. For IK a singularity is defined as a configuration of a kinematic chain where the rotation of any one joint does not result in the end-effector moving any closer to the goal.…”