Introduction Generating a trajectory for transportation systems in the envi- ronment containing obstacles requires to assure that carried load would not collide with another objects. If the overview of the scene is available, Voronoi diagram based method can be used for planning the safe path. However, acceleration during rapid movement can induce sways of a hanged object and cau- se a collision, therefore dynamic motion can not be used. Ge- nerally, oscillation excitation in crane transport systems and flexible mechanic parts of manipulators can negatively affect the speed of technology or manipulation process. To prevent the excitation of vibration in such slightly damped oscillatio- nal systems, generated control signal can be shaped by the ti- me delay convolution filter. Then the sway excitation is signi- ficantly suppressed and the hanged object better follows the overhead trolley path. Application of the convolution filter to the algorithm implies the change of a generated path. To preserve the safe characte- ristics of the path planning provided by the Voronoi diagram, overall time delay of the filter should be minimized. The re- search is focused on the online methods, insisting minimiza- tion of transient responses duration and parameter change ro- bustness. In presented feedforward scheme no complementary sensors are needed, but there is a significant influence of sys- tem identification, definition of possible parameters leakage and robust methods application. 1. System description Examined portal crane consist of an overhead trolley, positio- ned in horizontal plane and a load hanged on a cable of va- riable length. Positioning of the trolley is realized using the servo systems with feedback control structure, assuring desig- ned dynamics and suppression of outer disturbances. We ex- pect that generated desired trolley trajectory respects its dy- namic limitations, including the load influence. Pendulum character of a crane causes a yaw of the cable during the trol- ley acceleration and leads to load oscillations with slowly de- creasing amplitude. These oscillations are called residual vibrations. We expect tough control of trolley position, sup- pressing the influence of crane oscillations to the trolley. In the steady state, horizontal position of the crane corresponds to the trolley position, while during the dynamic movement large deflection is introduced. Fig. 1 presents a model of gantry crane moving in x direction. Payload of mass m is hanged on a cable of length L in a gravi- tational field of intensity g. Overhead trolley moves with acceleration a x . Angle between the cable and its settled positi- on is ϕ x and viscous friction is B. Transfer function describing the crane movement in x dimen- sion can be expressed as follows: (1) () 2 2 2 0 0 2 2 0 2 dt d s b s K s F x x a x x ϕ = ε ω + ω + ω = ε 108 RIADENIE MECHATRONICKÝCH SYSTÉMOV AT&P journal PLUS6 2005 Input shaping preventing the excitation of oscillation applied to the voronoi diagram planned path Peter Hubinský, Branislav Vranka Abstract This paper presents a path planning method suitable for control of oscillational 2D positioning systems preventing excitation of their vibration modes. It is based on application of input shaping methods to the Voronoi diagram planned desired path for movement in constrained space with obstacles. Filters for input shaping are numerically optimised to prevent big changes of the trajectory. Keywords: elimination, residual vibration, genetic algorithm, Voronoi diagram Fig.1 Sketch of a gantry crane