In this paper the minimum cost trajectory planning problem with fixed time in robot manipulators is considered. The task is solved by transforming the problem to a set of free right-end time optimal problems, leading to a suboptimal solution. Each problem of the optimal cost trajectory planning with a free time is effectively solved by the method of minimal neighbourhood. An algorithm for the task of suboptimal cost trajectory planning with fixed time is presented and applied to the model of a PUMA-like robot. Results of the paper seem to be of particular relevance to the optimization of multi-robot systems.