Tham khảo tài liệu 'control problems in robotics and automation - b. siciliano and . valavanis (eds) part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 160 c. Canudas de Wit Fig. . Two possible coordinate sets for the path following problem ble choices for the output variables describing the shorter signed distance between the points Al and Aỵ on the vehicle and the points Bl and Bl on the path. The other important coordinate is ỹ that describes the orientation difference between the path tangent at point Bt and the axis X attached to the vehicle. To make the discussion simpler assume that the steering angle a is the control input to be designed and V is the translational velocity. Then the simplified kinematic models expressed in the coordinates di 0 are di vsin a é v lsina- cos a d2 V cos a sin 6 Ó u sina Ji cos a cos where Ki is the radium of curvature of the path at point i. These models are valid locally as far as Ki s di 0. In many applications this hypothesis will hold since the radio of curvature of the path is likely to be large and the initial vehicle position will be close to the path. The variables di and d-2 are suitable choices because they correspond to system outputs that can be linearized in the spatial coordinates . flat outputs in the s-space . For instance for the model expressed in the di coordinates the control a arcsin fed 6 with the magnitude of kd smaller than one yields the following linear spatial equation d kd 0 where d 37- In the same sense as discussed before d will decrease as s will increase. Since in the path following problem the length of the path may not be limited or small as is the case for the parking maneuvers the spatial convergence induced by the above equation is particularly well adapted for Trends in Mobile Robot and Vehicle Control 161 the problem at hand. When d is small the control law indicates that a will tend to 0. Then the kinematic equation describing the variation of 0 tends to à __ V V V 7 sin a------77- i Ki s which indicates that the front wheel axis of the vehicle is orthogonal to the tangent to the path at point Bl. Remark . A similar study can be
