Transportation of objects using overhead cranes or manipulators can induce pendulum motion of the object. Residual oscillation from transportation typically must be damped or allowed to decay before the next process can take place. By properly programming the acceleration of the transporting device (e.g. crane) an oscillation damped transport and swing free stop is obtainable. This paper reviews the theory associated with oscillation damped trajectories for simply suspended objects and describes a particular implementation using a CIMCORP XR1100 gantry robot. IntroductionThis paper presents the mathematics describing oscillation damped trajectories for simply suspended payloads using controlled acceleration. In addition to the theoretical treatment, a specific hardware and software implementation currently in use at Sandia National Laboratories to generate oscillation damped trajectories is discussed. Finally, sources of error resulting in small residual oscillations are identified and possible solutions presented.Sandia National Laboratories is currently investigating the feasibility of using intelligent machines at nuclear waste storage sites. One class of operations that is necessary a t a waste storage site is the transportation of nuclear waste shipping casks and other heavy objects to various locations throughout the installation. During overhead crane transportation, an ,?bject is free Lo swing. If any oscillation of the object begins, the oscillation will have to be damped by the operator or the object allowed to swing until the amplitude of oscillation decays sufficiently to allow the next operation to begin. Either situation results in reduced facility availability. However, damping the oscillation of simply suspended payloads during transportation is possible if the acceleration of the crane or manipulator is programmable. Figure 1 is a simplified diagram of the transportation system under consideration. The transporting device moves in a horizontal direction (normal to gravity) while the simply suspended payload is free to oscillate about the pivot point 0. If the moving pivot point 0 undergoes a particular acceleration profile, the simply suspended payload will exhibit an oscillation damped transport and an oscillation damped stop. Figure 2 shows one acceleration profile for the moving pivot point 0 that can result in an oscillation a XR is a registered trademark of CIMCORP Inc. Mathematical FoundationFigure 1: Diagram of Transportation System damped trajectory for a simply suspended object. Point 0 has constant acceleration for time ta. After time ta, point 0 moves a t an intermediate constant velocity for time T. At time ( t o + T ) point 0 accelerates again with constant acceleration for time t.. T is selected such that the oscillation imposed on the object due to the second duration of acceleration is 180 degrees out of phase with initial oscillation of the swinging object, resulting in the object moving at constant velocity (during T ) without oscillation. After an arbitrary length of time FP, a...
Cranes used in the construction and transportation industries are generally devices with multiple degrees of freedom including variable load-line length, variable jib length (usually via a trolley), and variable boom angles. Point-to-point payload maneuvers using cranes are performed so as not to excite the spherical pendulum modes of their cable and payload assemblies. Typically, these pendulum modes, although time-varying, exhibit low frequencies. Current crane maneuvers are therefore performed slowly contributing to high construction and transportation costs. This investigation details a general method for applying command shaping to various multiple degree of freedom cranes such that the payload moves to a specified point without residual oscillation. A dynamic programming method is used for general command shaping for optimal maneuvers. Computationally, the dynamic programming approach requires order M calculations to arrive at a solution, where M is the number of discretizations of the input commands. This feature is exploited for the crane command shaping problem allowing for rapid calculation of command histories. Fast generation of commands is a necessity for practical use of command shaping for the applications described in this work. These results are compared to near-optimal solutions where the commands are linear combinations of acceleration pulse basis functions. The pulse shape is required due to hardware requirements. The weights on the basis functions are chosen as the solution to a parameter optimization problem solved using a Recursive Quadratic Programming technique. Simulation results and RECEIVED JON f 9 1995 experimental verification for a variable load-line length rotary crane are presented using both design procedures.
A jib crane consists of a pendulum-like end line attached to a rotatable jib. Within this general category of cranes there exist devices with multiple degrees of freedom including variable load-line length and variable jib length. These cranes are commonly used for construction and transportation applications. Point-to-point payload maneuvers using jib cranes are performed so as not to excite the spherical pendulum modes of their cable and payload assemblies. Typically, these pendulum modes, although time-varying, exhibit low frequencies. The resulting maneuvers are therefore performed slowly, contributing to high construction and transportation costs. The crane considered here consists of a spherical pendulum attached to a rigid jib. The other end of the jib is attached to a direct drive motor for generating rotational motion. A general approach is presented for determining the open-loop trajectories for the jib iotation for accomplishing fixed-time, point-to-point, residual oscillation free, symmetric maneuvers. These residual oscillation free trajectories purposely excite the pendulum modes in such a way that at the end of the maneuver the oscillatory degrees of freedom are quiescent. Simulation results are presented with experimental verification.
Angularly accelerating a cantilevered rod which sags under gravity couples the out-of-plane dynamics of the flexible rod and causes oscillation in both the horizontal and vertical planes. A parameter-scheduled trajectory planner has been analytically developed and experimentally implemented on a commercial robot t o suppress the first mode of these vibrations during a horizontal angular move. A load was attached t o the tip of the rod and the resulting static, out-of-plane, hub torque was measured with a force-torque sensor. This torque was used to predict the period of the horizontal first mode of vibration of the payload (rod and attached load) from a nonlinear function in order to calculate (schedule) the appropriate control parameters for the angular move. This system has been implemented on a Cincinnati Milacron T3-786* robot, and vibration suppressed trajectories (which reduce the coupled residual vibrations by over 90%) have been performed by the robot for various payloads.
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