Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator

Abstract

The goal of this paper is to present experimental results on the implementation of the damped least-squares method for the six-joint ABB IRb2000 industrial robot manipulator. A number of inverse kinematics schemes are reviewed which allow robot control through kinematic singularities. The basic schemes adopts a damped least-squares inverse of the manipulator Jacobian with a varying damping factor acting in the neighbor-hood of singularities. The effect of a weighted damped least-squares solution is investigated to provide user-defined accuracy capabilities along prescribed end-effector space directions. An on-line estimation algorithm is employed to measure closeness to singular configurations. A feedback correction error term is introduced to ensure algorithm tracking convergence and its effect on the joint velocity solution is discussed

Constrained resolved acceleration control for humanoids

“…9 and Eq. 13, respectively, are effective methods to perform trajectory conversion from taskspace to joint-space [16]. To a certain degree, the null space terms can be designed to perform secondary objectives such as keeping the robot away from kinematic constraints.…”

“…where K is a positive definite gain matrix and the vector e describes the orientation and position error between the desired and computed task descriptors [1], [16]:…”

IK-FA, a New Heuristic Inverse Kinematics Solver Using Firefly Algorithm

“…The pseudo inverse method replaces the Jacobian by its pseudo inverse, while it is not the exact inverse of J is still a good approximation. The main challenge with Jacobian inverse methods is how to compute to compute the Jacobian iteratively (Chiaverini et al, 1994;Buss, 2004).…”

“…The second class includes nature inspired techniques and hybrid techniques with learning capacities such as neural networks and neuro-fuzzy systems (Rutkowski et al, 2012;Juang, 2000;Zaidi et al, 2012;Pérez-Rodríguez et al, 2012) where the IK solver is observed as system with a set of inputs and output(s), the system needs first to be trained using a set of targets and solutions generally obtained using the forward kinematic model, it is then validated with a separate validation set and finally used. When the target point is far from the training set this systems generate limited precision solutions compared to Jacobian based conventional methods (Chiaverini et al, 1994;Buss, 2004); they are also time consuming and can not satisfy real time constraints (Zaidi et al, 2013;Pérez-Rodríguez et al, 2012).…”

“…Such inverse solvers should satisfy real-time constraints and should not suffer from any singularity which is not the case of classical IK solvers. Classical techniques consists in finding an approximation of the inverse kinematics of a system when the analytical expression of the inverse is complex and difficult to compute; this class of methods include the pseudo-inverse methods, the Jacobian transpose, the quasi Newton and the damped least square methods; classical inverse methods are time consuming essentially in systems with a high DOF (Chiaverini et al, 1994;Buss, 2004).…”