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Position-posture Control Strategy for Planar Underactuated Manipulators with Second-order Nonholonomic Constraint

Yawu Wang, Siyu Chen, and Pan Zhang*
International Journal of Control, Automation, and Systems, vol. 20, no. 12, pp.4015-4025, 2022

Abstract : For a planar underactuated manipulator (PUM), if one of its joints is passive except for the first joint, it has the second-order nonholonomic constraint. This paper develops a novel control approach for such PUMs. Combining with the geometry relationship of the PUM and using differential evolution algorithm (DEA), the desired angles of all joints are solved, which transforms the position-posture control into the angle control. The coupling relationship between the passive joint and all active joints is developed, which indicates that the passive joint angle can be adjusted jointly to its desired value when all active joints rotate to their desired angles along specific trajectories. Then, the trajectories for all active joints are constructed, and their design parameters are solved by using the DEA. The continuous state feedback controllers are designed for all active joints to make them track their trajectories. Taking four-link PUMs with one passive joint located at different positions as examples, we perform four simulations and the results verify the universality and superiority of the above approach.

Keyword : Continuous state feedback controller, differential evolution algorithm, planar underactuated manipulator, position-posture control, second-order nonholonomic constraint.

 
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