Modified virtual decomposition control for robotic mechanisms with mixed kinematic chains: a fully decentralized control algorithm

Conventional virtual decomposition control (VDC) is a Newton–Euler formulation-based distributed adaptive control algorithm dealing with complex robotic systems. However, the VDC has the following characteristics. Firstly, the algorithm should be implemented recursively, assuming a known force/moment transformation matrix. Secondly, the local stability of each subsystem can be proved using the virtual power flow concept, which ensures the entire system’s stability. Therefore, this paper proposes a fully decentralized control algorithm as an alternative to the conventional VDC. The key idea is to design an estimator for the coupling interconnection term. In addition, this work avoids using the concept of virtual power flow as a constraint (condition) for proving the virtual stability of the individual subsystem. Adaptive approximation control is used as a basis for control architecture. Besides, the proposed controller is applicable to mixed open/closed-chain mechanisms. For a closed-chain mechanism subsystem, the problem is formulated as the minimization of the actuator torques with equality constraints (in the case of over-actuation). A direct solution is obtained for an open-chain subsystem. We present symbolic calculations for some robots with a kinematic loop to clarify the proposed modeling procedure. Simulations are performed for a 6-link biped robot with two kinematic chain configurations to investigate the proposed algorithm’s effectiveness. In addition, a comparative analysis is performed to prove the validity of the results.