{"responseHeader":{"status":0,"QTime":8,"params":{"q":"{!q.op=AND}id:\"97649\"","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":"/e0/e6/e0e6b746159c0b702c0051bdb57a996d9500145a.jpg","oldid_t":"compsci 5762","setname_s":"ir_computersa","restricted_i":0,"format_t":"application/pdf","modified_tdt":"2016-04-27T00:00:00Z","file_s":"/c4/b6/c4b61a0945a76da07530ebc51f5281aab234a2a7.pdf","title_t":"Page 23","ocr_t":"9 2.2 Spacetime Constraints and Related Work 2.2.1 Spacetime Constraints vVitkin and Kass' [56] work overcame the restrictions of specifying initial value problems inherent in dynamic simulation by simultaneously solving for entire motion sequences. By raising the dimensionality of the problem from sequentially solving for single points in time, to one seeking an integral solution in space and time, it is possible to specify and generate more complex behaviors. The key difference between spacetime solutions and dynamic simulation is a shift in the definition of the set of unknowns. In forward dynamic simulation, the set of unknowns at each time step consists of the degrees of freedom of the linked figure. A degree of freedom in this context is an angle (for a revolute DOF) or a position (for a translational DOF). For example, a simple revolute joint such as an elbow defines one DOF, while a ball and socket joint with three axes of revolution defines three DOF. The active forces plus the current state of the system, (positions and velocities of the DOF), provide the information to solve for the changes in the DOF in the next time step. Motion sequences are then produced by integrating these changes over time. In contrast, the unknown DOF in a spacetime solution consist of ALL the inherent degrees of freedom of the creature, plus the relevant forces, for ALL time steps simultaneously. Thus, one seeks a solution for an entire motion sequence in a single solution process. The solution process consists of iteratively optimizing an objective function subject to a set of constraints. Alternatively, the unknowns can be thought of as a set of functions of time as opposed to a set of scalar values at a point in time. Witkin and Kass discussed two types of constraints. The first were constraints derived from physics, i.e., differential equations that relate the forces to the acceleration (second derivative) of position. The other type of constraint was a user","id":97649,"created_tdt":"2016-04-27T00:00:00Z","parent_i":97747,"_version_":1642982591101403136}]},"highlighting":{"97649":{"ocr_t":[]}}}