tailieunhanh - Humanoid Robots - New Developments Part 9

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 . how much the robot wants to repeat what it has observed. We chose values of gp and gv in the range 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 .