A novel approach for tip tracking control of a horizontal tensegrity continuum robot with slack cables

Tensegrity continuum robots (TCRs) are an emerging class of flexible continuum robots that employ the tensegrity concept to achieve a natural balance of compliance and strength. The dynamics of a TCR with slack cables is a high-dimensional non-smooth nonlinear system. Motion control of such a system is challenging, especially when the TCR is placed horizontally. In this work, a differential–algebraic equations (DAEs) model-based instantaneous optimal control (IOC) approach for the tip’s position and orientation collaborative tracking of a horizontal TCR with slack stiffening cables is proposed. Based on the complementarity theory and the Fischer–Burmeister function, the non-smooth problem of cable relaxation can be described as a continuous differentiable algebraic equation. Then, by combining the dynamic differential equations, a DAEs model of the TCR with slack cables can be obtained. Subsequently, the original continuous tip tracking problem is approximated to a series of IOC problems at each discrete time slot. Finally, considering the control input saturation constraints, a suboptimal control law can be obtained just by solving a small-scale optimization problem. The proposed IOC approach provides a novel and unified control framework to deal with the tip tracking problem of the horizontal TCRs, and the non-smooth property of cable relaxation is naturally involved in the IOC controller. Numerical experiments on the tip tracking of a horizontal TCR are conducted to demonstrate the effectiveness and advantages of the proposed IOC method.