To be competitive, an industrial robot picking fruits must be able to perform this task in an amount of time which compares to that needed by humans. Because the location of a fruit changes due to the picking of others, the determination of their location has to be performed on-line and also the associated path planning for the robot. This poses two major problems in the development of fruit-picking robots since locating fruits and path planning, in general, are computationally expensive operations. This paper contributes to relaxing the second problem. Using the fact that the motions of the links of an industrial robot are approximately decoupled, this paper proposes a new method for near minimum-time path planning and control in the presence of obstacles. This method is computationally cheap compared to methods that solve the more general problem. Experimental results are presented which indicate the feasibility of this approach to make the robot competitive.