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.

This paper addresses the stiffness estimation problem for flexible robot joints, driven by variable stiffness actuators in antagonistic setups. Due to the difficulties of achieving consistent production of these actuators and the time-varying nature of their internal flexible elements, which are subject to plastic deformation over time, it is currently a challenge to precisely determine the total flexibility torque applied to a robot's joint and the corresponding joint stiffness. Herein, by considering the flexibility torque acting on each motor as an unknown signal and building upon Unknown Input Observer theory, a solution for electrically-driven actuators is proposed, which consists of a linear estimator requiring only knowledge about the positions of the joints and the motors as well as the drive's dynamic parameters. Beyond its linearity advantage, another appealing feature of the solution is the lack of need for torque and velocity sensors. The presented approach is first verified via simulations and then successfully tested on an experimental setup, comprising bidirectional antagonistic variable stiffness actuators.

Despite having proven successful in generating precise motions under dynamic conditions in highly deformable soft-bodied robots, model based techniques are also prone to robustness issues connected to the intrinsic uncertain nature of the dynamics of these systems. This letter aims at tackling this challenge, by extending the augmented rigid robot formulation to a stable representation of three dimensional motions of soft robots, under Piecewise Constant Curvature hypothesis. In turn, the equivalence between soft-bodied and rigid robots permits to derive effective adaptive controllers for soft-bodied robots, achieving perfect posture regulation under considerable errors in the knowledge of system parameters. The effectiveness of the proposed control design is demonstrated through extensive simulations.

The control of articulated soft robots, i.e. robots with flexible joints and rigid links, presents a challenge due to their intrinsic elastic elements and nonlinear force-deflection dependency. This letter first proposes a discrete-time delayed unknown input-state observer based on a nominal robot model that reconstructs the total torque disturbance vector, resulting from the imperfect knowledge of the elastic torque characteristic, external torques, and other model uncertainties. Then, it introduces a robust controller, that actively compensates for the estimated uncertainty and allows bounded stability for the tracking of independent link position and joint stiffness reference signals. The convergence of the disturbance estimator and the overall system’s stability in closed loop is proven analytically, while the effectiveness of the proposed control design is first evaluated in simulations with respect to large uncertainty conditions, and then demonstrated through experiments on a real multi-degree-of-freedom articulated soft robot.

Currently, the access to the knowledge of stiffness values is typically constrained to a-priori identified models or datasheet information, which either do not usually take into account the full range of possible stiffness values or need extensive experiments. This work tackles the challenge of stiffness estimation in articulated soft manipulators, and it proposes an innovative solution adding value to the previous research by removing the necessity for force/torque sensors and generalizing to multi-degree-of-freedom robots. Built upon the theory of unknown input-state observers and recursive least-square algorithms, the solution is independent of the actuator model parameters and its internal control signals. The validity of the approach is proven analytically for single and multiple degree-of-freedom robots. The obtained estimators are first evaluated via simulations on articulated soft robots with different actuations and then tested in experiments with real robotic setups using antagonistic variable stiffness actuators.

This letter investigates the stability properties of the soft inverted pendulum with affine curvature - a template model for nonlinear control of underactuated soft robots. We look at how changes in physical parameters affect stability and equilibrium. We give conditions under which zero dynamics corresponding to a collocated choice of the output is (locally or globally) stable or unstable. We leverage these results to design a switching controller that stabilizes a class of nonlinear equilibria of the pendulum, which can drive the system from one equilibrium to another.