In this paper, study results of the trajectory planning algorithms of industrial robot manipulators are presented. A classification of various robotic manipulators’ trajectory planning algorithms is proposed, and various time and time-energy optimal control algorithms are analyzed. Planning algorithms are categorized in direct and iterative methods, either with new trajectory generation or motion control along predefined Cartesian robot path. Time-variable or time-constant methods are distinguished. A review of various cost functions of iterative solutions is given and the stated numerical results are compared. Among direct methods 4 different acceleration profile types of point-to-point movements, each within 3 different axes’ synchronization alternatives have been simulated by means of energy and time efficiency and compared with a trajectory generated of an RCS module of a KUKA KR2210 industrial robot.