Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space
Delta parallel robots have been widely used in precision processing, handling, sorting, and the assembly of parts, and their high efficiency and motion stability are important indexes of their performance.Corners created by small line segments in trajectory planning cause abrupt changes in a tangent...
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MDPI AG
2023-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/21/4509 |
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| author | Dachang Zhu Yonglong He Xuezhe Yu Fangyi Li |
| author_facet | Dachang Zhu Yonglong He Xuezhe Yu Fangyi Li |
| author_sort | Dachang Zhu |
| collection | DOAJ |
| description | Delta parallel robots have been widely used in precision processing, handling, sorting, and the assembly of parts, and their high efficiency and motion stability are important indexes of their performance.Corners created by small line segments in trajectory planning cause abrupt changes in a tangential discontinuous trajectory, and the vibration and shock caused by such changes seriously affect the robot’s high-speed and high-precision performance. In this study, a trajectory-planning method combining Cartesian space and joint space is proposed. Firstly, the vector method and microelement integration method were used to establish the complete kinematic and dynamic equations of a delta parallel robot, and an inverse kinematic/dynamic model-solving program was written based on the MATLAB software R2020a. Secondly, the end-effector trajectory of the delta parallel robot was planned in Cartesian space, and the data points and inverse control points of the end effector’s trajectory were obtained using the normalization method. Finally, the data points and control points were mapped to the joint space through the inverse kinematic equation, and the fifth-order B-spline curve was adopted for quadratic trajectory planning, which allowed the high-order continuous smoothing of the trajectory planning to be realized. The simulated and experimental results showed that the trajectory-smoothing performance in continuous high-order curvature changes could be improved with the proposed method. The peak trajectory tracking error was reduced by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>10.53</mn><mo>%</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>41.18</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>44.44</mn><mo>%</mo></mrow></semantics></math></inline-formula>, respectively, and the peak torque change of the three joints was reduced by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.5</mn><mo>%</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>11.6</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.6</mn><mo>%</mo></mrow></semantics></math></inline-formula>, respectively. |
| first_indexed | 2024-03-11T11:25:52Z |
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| id | doaj.art-f6ba353f2e3c4cadadbba6a74358130a |
| institution | Directory Open Access Journal |
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| language | English |
| last_indexed | 2024-03-11T11:25:52Z |
| publishDate | 2023-11-01 |
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| spelling | doaj.art-f6ba353f2e3c4cadadbba6a74358130a2023-11-10T15:08:07ZengMDPI AGMathematics2227-73902023-11-011121450910.3390/math11214509Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint SpaceDachang Zhu0Yonglong He1Xuezhe Yu2Fangyi Li3School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, ChinaDelta parallel robots have been widely used in precision processing, handling, sorting, and the assembly of parts, and their high efficiency and motion stability are important indexes of their performance.Corners created by small line segments in trajectory planning cause abrupt changes in a tangential discontinuous trajectory, and the vibration and shock caused by such changes seriously affect the robot’s high-speed and high-precision performance. In this study, a trajectory-planning method combining Cartesian space and joint space is proposed. Firstly, the vector method and microelement integration method were used to establish the complete kinematic and dynamic equations of a delta parallel robot, and an inverse kinematic/dynamic model-solving program was written based on the MATLAB software R2020a. Secondly, the end-effector trajectory of the delta parallel robot was planned in Cartesian space, and the data points and inverse control points of the end effector’s trajectory were obtained using the normalization method. Finally, the data points and control points were mapped to the joint space through the inverse kinematic equation, and the fifth-order B-spline curve was adopted for quadratic trajectory planning, which allowed the high-order continuous smoothing of the trajectory planning to be realized. The simulated and experimental results showed that the trajectory-smoothing performance in continuous high-order curvature changes could be improved with the proposed method. The peak trajectory tracking error was reduced by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>10.53</mn><mo>%</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>41.18</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>44.44</mn><mo>%</mo></mrow></semantics></math></inline-formula>, respectively, and the peak torque change of the three joints was reduced by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.5</mn><mo>%</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>11.6</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.6</mn><mo>%</mo></mrow></semantics></math></inline-formula>, respectively.https://www.mdpi.com/2227-7390/11/21/4509delta parallel robotkinematic and dynamic modellingtrajectory smoothing planningcombining Cartesian space with joint space |
| spellingShingle | Dachang Zhu Yonglong He Xuezhe Yu Fangyi Li Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space Mathematics delta parallel robot kinematic and dynamic modelling trajectory smoothing planning combining Cartesian space with joint space |
| title | Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space |
| title_full | Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space |
| title_fullStr | Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space |
| title_full_unstemmed | Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space |
| title_short | Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space |
| title_sort | trajectory smoothing planning of delta parallel robot combining cartesian and joint space |
| topic | delta parallel robot kinematic and dynamic modelling trajectory smoothing planning combining Cartesian space with joint space |
| url | https://www.mdpi.com/2227-7390/11/21/4509 |
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