The problem of optimal control of robotic manipulators is dealt with in two stages: (1) optimal trajectory planning, which is performed off-line and results in the prescription of the position and velocity of each link as a function of time along a “given” path and (2) on-line trajectory tracking, during which the manipulator is guided along the planned trajectory using a feedback control algorithm. In order to obtain a general trajectory planning algorithm which could account for various constraints and performance indices, the technique of dynamic programming is adopted. It is shown that for a given path, this problem is reduced to a search over the velocity of one moving manipulator link. The design of the algorithm for optimal trajectory planning and the relevant computational issues are discussed. Simulations are performed to test the effectiveness of this method. The use of this algorithm in conjunction with an on-line controller is also presented.
We described four offspring of a consanguineous couple with arterial tortuosity "syndrome" (ATS). The affected children had extensive arterial involvement although the clinical presentations were quite variable. Clinical manifestations included cutis laxa or soft/thin skin, joint laxity or contractures, and arachnodactyly. Aortic tortuosity and pulmonary artery aneurysms with or without peripheral stenoses were demonstrated in all four sibs. All three males had inguinal hernias. Inconsistent facial anomalies were downslanting palpebral tissues, beaked nose, micrognathia, and high-arched palate. Results of collagen type I and type III biosynthesis studies were normal on skin fibroblasts. Histologic findings on autopsy of one affected child showed arterial changes with disruption of elastic fibers of the media and fragmentation of the internal elastic membrane as well as mucosal and transmural necrosis of the stomach, small bowel, colon, and extensive necrosis of the liver. Coronary artery involvement was also seen in this child as well as biventricular hypertrophy. We conclude that ATS is an autosomal recessive connective tissue condition associated with diffuse arterial changes and involvement of the skin, joints, and other organs.
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