A computationally efficient algorithm for determining the motion sequence of a citrus picking robot that allows the picking time to be minimized was developed. The suggested algorithm can be applied in real-time. The sequence of motions was obtained from the solution of the travelling salesman problem (TSP) using the total distance travelled along near-minimum-time paths between all fruit locations as the cost function to be minimized. This cost function takes into consideration both the inertial properties and kinematic structure of the robot manipulator. Simulation results for a cylindrical type of robot for twenty measured citrus trees indicate that the mode of travel through the tree is influenced by the geometric shape of the tree. The optimal path between consecutive fruit locations depends on the inertial parameters of the robot. Dividing the tree into subvolumes reduces the computation time required by the algorithm. Travelling vertically through the tree's subvolumes reduces the picking time as compared to horizontal travel. The suggested algorithm can serve as a basis for comparing the performance of different robots and can help in selecting the most efficient robot design for any given harvesting task.