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Vision-based Pythagorean hodograph spline command generation and adaptive disturbance compensation for planar contour tracking

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Abstract

Many control problems encountered in industrial applications such as deburring, cutting, and polishing are required to simultaneously perform force control and contour following. If the mathematical model of the contour to be followed is known, then the control problem is straightforward, and many existing approaches can be used to tackle this problem. In contrast, if the mathematical model is not available, the control problem will become much more challenging. Among all possible solutions to circumvent the aforementioned difficulties, using a vision system to obtain the mathematical model of the contour to be followed is one of the best options. To this end, this paper proposes a vision-based approach, in which a vision system is employed to provide the exterior contour information of the object for machining. Subsequently, coordinate transformation between the image plane and the robot frame is performed. Based on the exterior contour information after coordinate transformation, a Pythagorean hodograph quintic spline interpolator based on S curve acceleration/deceleration is developed to generate motion commands. The fact that the arc length of a Pythagorean hodograph curve can be easily computed makes it particularly useful when performing motion planning for high-precision motion control systems. Moreover, in order to improve contour following accuracy, an integrated motion control structure consisting of an adaptive disturbance compensator, a sliding mode controller, and a friction compensator is also developed. Finally, several contour following experiments are conducted by a planar two-link robot manipulator to verify the effectiveness of the proposed approach.

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Authors and Affiliations

  1. Department of Electrical Engineering, National Cheng Kung University, No. 1, Ta-Hsueh Road, Tainan, 701, Taiwan, Republic of China

    Chao-Yun Chen, Shang-Shiun Shieh, Ming-Yang Cheng & Ke-Han Su

Authors
  1. Chao-Yun Chen
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  2. Shang-Shiun Shieh
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  3. Ming-Yang Cheng
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  4. Ke-Han Su
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Corresponding author

Correspondence to Ming-Yang Cheng.

Appendix

Appendix

Fig. 12
figure 12

S curve ACC/DEC motion planning; T A acceleration (deceleration) duration, T B maximum acceleration duration, T S maximum speed duration, A max maximum acceleration, V max maximum velocity, L max total moving distance. T A  = V max/A avg, T B  = 2V max/A max − T A , T C  = (T A  − T B )/2, T S  = (L max − V max T A )/V max. By giving the values of A max, V max, L max, and the average acceleration A avg, one can determine the values of T A , T B , T C , and T S

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Chen, CY., Shieh, SS., Cheng, MY. et al. Vision-based Pythagorean hodograph spline command generation and adaptive disturbance compensation for planar contour tracking. Int J Adv Manuf Technol 65, 1185–1199 (2013). https://doi.org/10.1007/s00170-012-4250-9

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  • DOI: https://doi.org/10.1007/s00170-012-4250-9

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