HAN Jiang, WANG Peng, DONG Fangfang, XIA Lian, CHEN Shan, LU Lei. Modeling and Control of Planar Redundant Parallel Robots Based on the Udwadia-Kalaba Method[J]. Applied Mathematics and Mechanics, 2020, 41(11): 1183-1196. doi: 10.21656/1000-0887.400363
 Citation: HAN Jiang, WANG Peng, DONG Fangfang, XIA Lian, CHEN Shan, LU Lei. Modeling and Control of Planar Redundant Parallel Robots Based on the Udwadia-Kalaba Method[J]. Applied Mathematics and Mechanics, 2020, 41(11): 1183-1196.

# Modeling and Control of Planar Redundant Parallel Robots Based on the Udwadia-Kalaba Method

##### doi: 10.21656/1000-0887.400363
Funds:  The National Key R&D Program of China（2018YFB1308400）;The National Natural Science Foundation of China（51905140）
• Rev Recd Date: 2020-03-01
• Publish Date: 2020-11-01
• The redundantly driven parallel robots were considered. The Udwadia-Kalaba (U-K) method was used to formulate the physical connections of the parallel mechanism as system constraints, and the closed-chain motion equations for the planar 2-DOF redundantly driven parallel robot were established. Firstly, the 2-DOF robot was divided into 3 unconstrained open-chain subsystems. The dynamic equations for the subsystems were obtained with the Lagrangian method. Then, the kinematic constraints were used to describe the physical connections between each subsystem and the end effector, and between each subsystem and the base. The constraint was differentiated and transformed into a 2nd-order Pfaffian standard differential form. With the U-K equations, the analytical solution satisfying the physical constraints was given. According to the U-K theory, the constraints can be added to the unconstrained open-chain system equations to establish the dynamics model for the planar redundantly driven parallel robot. In the trajectory tracking controller design, the desired position or velocity trajectory was formulated as a virtual constraint, and the constraint condition was transformed into a standard Pfaffian differential form. Then the U-K equations were used to solve the output torque required for each driving joint to satisfy a given trajectory constraint. This method does not require auxiliary variables such as Lagrangian multipliers or pseudo-generalized speeds, and can handle both holonomic and non-holonomic constraints. The numerical simulation and analysis results show that, the modeling and controlling method can effectively, systematically and quickly establish the dynamic analytical decoupling model for the planar 2-DOF redundantly driven parallel robot, and realize the high-precision tracking control along a given trajectory.
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