The synthesis of smooth trajectories for pick-and-place operations

J. Angeles, A. Alivizatos, P.J. Zsombor-Murray
1988 IEEE Transactions on Systems, Man and Cybernetics  
Ahtruct -A spline-based method of programming smooth trajctories for pick-and-place operations is introduced. Unlike continuous-path operation*, which impose a unique Cartesian trajectoq, an infinite number of 5niooth trajectories can be described between any given pick and its corresponding place configuration. The method presented here allows one the construction of a unique C2 -continuous pick-and-place trajectory with attractive features. The method begins with the mapping of the pick and
more » ... g of the pick and the place configurations in Cartesian space into joint-coordinate space, using a general-purpose inverse kinematics package that handles singularitie* and redundancies. Next, a trajectory, composed of a C'-continuous, periodic cubic 5pline segment, is defined between the pick and the place configurations in the joint-coordinate space. It is demonstrated that C? -continuity will prevail in Cartesian space as well. The software implementing this method includes a graphics package, to render and animate the robot motion display, as well as an interface to an off-line programniing system to realize the synthesis of the actual robot motion. Finally, details of the procedure are illustrated with a numerical example applied to a commercial industrial robot. Abstract -The technique of fuzzy reasoning via transformatiom of fuzzy truth state vectors by fuzzy rule matrices is extended to Petri netr. The result is a new type of neural network where the Wansition bar5 serve as the neurons, and the nodes are conditions. Condition5 may be conjuncted and disjuncted in a natural way to allow the firing of the neuronc,. Such conjuncting of truths is executed as generalized ANriing. i.e., mxing. Modifications are made to the usual Petri model to allow fuzzy rule-bawd reasoning by propositional logic. First, fuzzy values are allowed for rule5 and truths of conditions that appear in rules. Next, multiple copies, rather than the original, of the fuzzy truth tokens are passed along all arrow\ that depart a node or transition bar where the truth token resides. An algorithm is presented for reasoning via these networks, as well as a simple example for exercising the algorithm. Abduction may be done analogously by reversing all arrows and propagating truth tokens backwards.
doi:10.1109/21.87066 fatcat:5ng6hp6injgshgu4kedhd7le34