{"responseHeader":{"status":0,"QTime":8,"params":{"q":"{!q.op=AND}id:\"97731\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"file_name_t":"Cohen-Spacetme_Control.pdf","thumb_s":"/05/23/0523dbcd34e4d9e2c0797d790bd781000daaa0b3.jpg","oldid_t":"compsci 5844","setname_s":"ir_computersa","restricted_i":0,"format_t":"application/pdf","modified_tdt":"2016-04-27T00:00:00Z","file_s":"/db/ba/dbba34efd0cecf6789cddae1862be9c0e45646f5.pdf","title_t":"Page 105","ocr_t":"91 Finally, by removing all the DOF except the ball position from the spacetime window, the iterations became very fast. 6.6.4 Subexpressions and Objective Functions Three different definitions of objectives were used with similar resulting aniĀmations. The first involved explicit inclusion of torques as additional DOF. The torques were constrained to be equated with the differential equations of motion through physical laws. The objective was then set to minimize the torques over time. The animation of the throw resulted in 151 constraint instances and 216 control points. The Langrangian Hessian contained 2143 nonzero entries (or 1.59% sparseness). Iterations took 15.9 seconds on average. In the second trial, the torques were included as subexpressions, thus lowering the number of DOF and constraints. In this case, the same animation required only 70 constraint instances and 135 control points. However, the denser matrix, with 985 entries (2.34% sparseness) required 13.0 seconds per iteration. Although the system of equations was much smaller, the increased complexity of each symbolic expression and thus the increased time required to evaluate the Hessian, reduced the computational savings. The third set of objectives included approximating the torques by the second derivatives of the joint angles weighted by the static moment of the links beyond the joints. This resulted in the same number of constraints and control points but the iterations took only 4.55 seconds due the the elimination of the inertial terms in the objective. There were no subjective differences in the resulting animation, although further study would probably be required to draw firm conclusions. 6.6.5 Catch and Throw An extended sequence was created that included the arm catching and then throwing the ball. The set of constraints and objectives were very similar to those","id":97731,"created_tdt":"2016-04-27T00:00:00Z","parent_i":97747,"_version_":1642982591128666115}]},"highlighting":{"97731":{"ocr_t":[]}}}