Trajectory optimization of a mining dragline using the method of Lagrange multipliers

The nonlinear coupled dynamic behaviour of a mining dragline is optimized to increase productivity and reduce metal fatigue on the boom. Draglines are very large crane-like robots used in open cut mining, primarily for the removal of overburden that covers a coal seam. The dynamic behaviour of the machine is a key determinant of productivity and fatigue-based maintenance. The Newton-Lagrange method is applied to a field-validated model to optimize slew torque under nonlinear constraints. Two scenarios are analysed: the minimization of cycle time with a time penalty for duty (estimated fatigue damage) and fixed rope lengths, and the minimization of duty under a fixed cycle time and measured rope lengths. The results from the second scenario compare favourably with earlier efforts to optimize slew torque using intuitive manual techniques. In particular, the numerical optimization procedure achieved a 50-60% reduction in duty, improving upon manual optimization results by 10-30%. Techniques are presented for solving convergence issues related to the high degree of nonlinearity of the model and constraints, actuator limitations and noise introduced by measured data