Well-conditioned configurations of fault-tolerant manipulators

Fault-tolerant motion of redundant manipulators can be obtained by joint velocity reconfiguration. For faulttolerant manipulators, it is beneficial to determine the configurations that can tolerate the locked-joint failures with a minimum relative joint velocity jump. This is because the manipulator can rapidly reconfigure itself to tolerate the fault. This paper uses the properties of condition numbers to introduce those optimal configurations for serial manipulators. The relationship between the manipulator’s locked-joint failures and the condition number of the Jacobian matrix is indicated by using a matrix perturbation methodology. It is observed that the condition number provides the upper bound of required relative joint velocity change for recovering the faults which leads to define the optimal fault-tolerant configuration from the minimization of the condition number. The optimization problem to obtain the minimum condition number is converted to three standard Eigen value optimization problems. Finally, in order to obtain the optimal fault-tolerant configuration, the proposed method is applied to a 4-DoF planar manipulator.