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Tham khảo tài liệu 'humanoid robots - new developments part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 272 Humanoid Robots New Developments vi is the velocity out of Pi scaled by an arbitrary factor and ữị is a scalar indicating the magnitude of the acceleration. The direction of the acceleration is deducible from Tị which is a quaternion describing the change in direction between Vị and Vị-1 as a rotation through their mutually orthogonal axis. Fig. 5. Datapath in the learning algorithm arrows and execution sequence numbers . Previously observed trajectory Pi-1 Prediction Fig. 6. Trajectory prediction using a prototype. The progression of a trajectory pk k e N at a given instant may be predicted using a prototype. Suppose that for a particular trajectory sample p j it is known that Pi Sticky Hands 273 corresponds best to p j then p j aiTi .p j -p j-1 is an estimate for p j 1 . Premultiplication of a 3-vector by T denotes quaternion rotation in the usual way. This formula applies the bend and acceleration occurring at pi to predict the position of p j . We also linearly blend the position of pi into the prediction and the magnitude of the velocity so that p j combines the actual position and velocity of pi with the prediction duplicating the bending and accelerating characteristics of pi see Fig. 6 p j - p j _1 7 P j 1 P j SjTi gp pi - P j p j - p j-11 sj 1 - gv ai p j -p j-1 gv vi 8 g p and g v are blending ratios used to manage the extent to which predictions are entirely general or repeat previously observed trajectories i.e. how much the robot wants to repeat what it has observed. We chose values of gp and gv in the range 0.1 0.001 through empirical estimation. g p describes the tendency of predictions to gravitate spatially towards recorded motions and g v has the corresponding effect on velocity. In the absence of a corresponding prototype we can calculate P j-1 and use it to estimate p j 1 thus extrapolating the current characteristics of the trajectory. Repeated extrapolations lie in a single plane determined by pi-2 pi-1 and pi and maintain the trajectory .
