The paper presents an application of Interval Newton method to solve the inverse kinematics and redundancy resolution of a serial redundant manipulator. Such inverse problems are often encountered when the manipulator link lengths, joint angles and end-effector uncertainty bounds are given, which occurs due to because of inaccuracies in joint angle measurements, manufacturing tolerances, link geometries approximations, etc. The inverse kinematics of three degree of freedom planar redundant positioning manipulator without end-effector has been evaluated using the manipulability of Jacobian matrix as performance metric. To solve the nonlinear equation of inverse kinematics, the multidimensional Newton method is used. The inverse kinematics is intended to produce solutions for joint variables in interval of tolerances for specified end effector accuracy range. As exemplar problem solving, a planar 3-degrees-of-freedom serial link redundant manipulators is considered.

The aim here remains to introduce effectiveness of interval methods in analyzing dynamic uncertainties for marine navigational sensors. The present work has been carried out with an integrated sensor suite consisting of a low cost MEMs inertial sensor, GPS receiver of moderate accuracy, Doppler velocity profiler and a magnetic fluxgate compass. Error bounds for all the sensors have been translated into guaranteed intervals. GPS based position intervals are fed into a forward-backward propagation method in order to estimate interval valued inertial data. Dynamic noise margins are finally computed from comparisons between the estimated and measured inertial quantities It has been found that the intervals as estimated by proposed approach are supersets of 95% confidence levels of dynamic errors of accelerations. This indicates a significant drift of dynamic error in accelerations which may not be clearly defined using stationary error bounds. On the other side bounds of non-stationary error for rate gyroscope are found to be in consistence with the intervals as predicted using stationary noise coefficients. The guaranteed intervals estimated by the proposed forward backward contractor, are close to 95% confidence levels of stationary errors computed over the sampling period.