tailieunhanh - Humanoid Robots Human-like Machines Part 14

Tham khảo tài liệu 'humanoid robots human-like machines part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Bilinear Time Delay Neural Network System for Humanoid Robot Software 511 Figure 14. Kinematics neural network d2 xi dxi xi -77- d0j dỡjdỡk dejdekdel d2 xi 23 Fig. 15 show the growing neural network in this process. 2 O3 a 1st order terms of the Polynomial x y z 01 x b A part of 2nd order terms of the Polynomial 01 x c A part of 3rd order terms of the Polynomial Figure 15. Kinematics neural network by learning process 512 Humanoid Robots Human-like Machines Inverse Kinematics In this sub-section I discuss the inverse kinematics problem. In this problem the solution has an inverse trigonometric function. 1 2Z Z. I 2 z 24 2 Analytical Method The inverse kinematics of the arm has 4 type solutions. In this sub-section I only discuss following solution. The other solutions can be considered in the similar way. 61 tan-1 y 63 cos -1 -1 62 cos a r In the similar fashion as the forward kinematics there is a convergence radius problem of the Taylor expansion of the term 1 y tan 1 x y cos 1 z I r . It can be avoidable using the concept of analytical continuation. For example because the function tan 1 x y has the singular points at i the expansion near x y 0 breaks down near 1 . show the example of region splitting for tan 1 x y . Such techniques keep a high accuracy for wide range. Fig. 17 shows a part of the neural network using such techniques. It includes the digital switch neuron. Figure 16. Approximate solution of 6 tan-1 y Bilinear Time Delay Neural Network System for Humanoid Robot Software 513 Numerical Method If we do not have the information of arm the above technique can be applied numerically. In this case the neural network has the some polynomials with digital switch . z Figure 17. A part of inverse kinematics neural network Motion Generation and Control There are many references about the motion generation and control using this system. See references Nagashima 2003 . Fig. 18 show the example of growing neural .