This article is concerned with the fixed-time path-following control problem of a perturbed cart-pendulum robot with linear quadratic (LQ) performance optimization. In order to ensure the displacements of cart and pendulum of the robot following the desired paths within fixed-time, adaptive anti-perturbation sliding mode control schemes with a novel fixed-time sliding mode surface are developed to withstand the adverse influence of perturbations. Furthermore, an adaptive radial basis function neural network (RBFNN)-based sliding mode control algorithm is employed to approximate the continuous perturbations, so that the path-following LQ control problem can be further dealt with. The fixed-time stability and path-following results of the cart-pendulum robotic system are achieved by Lyapunov stability theory. A simulation example for a heavy material handling agricultural robot is proposed to verify the effectiveness of the developed method.