Decoupled nonlinear adaptive control of position and stiffness for pneumatic soft robots

This article addresses the problem of simultaneous and robust closed-loop control of joint stiffness and position, for a class of antagonistically actuated pneumatic soft robots with rigid links and compliant joints. By introducing a first-order dynamic equation for the stiffness variable and using the additional control degree of freedom, embedded in the null space of the pneumatic actuator matrix, an innovative control approach is introduced comprising an adaptive compensator and a dynamic decoupler. The proposed solution builds upon existing adaptive control theory and provides a technique for closing the loop on joint stiffness in pneumatic variable stiffness actuators. Under a very mild assumption involving the inertia and actuator matrices, the solution is able to cope with uncertainties of the model and, when the desired stiffness is constant or slowly varying, also of the pneumatic actuator. Position and stiffness decoupling is achieved by the introduction of a first-order differential equation for an internal state variable of the controller, which takes into account the time derivative of pressure in the stiffness dynamics. A formal proof of the stability of the position and stiffness tracking errors is provided. An appealing property of the approach is that it does not require higher derivatives of position or any derivatives of stiffness. The solution is validated with respect to several use-cases, first in simulation and then via a real pneumatic soft robot with McKibben muscles. A comparison with respect to existing techniques reveals a more robust position and stiffness tracking skill.