This paper proposes a new semi-analytical design and implementation method for nonlinear partial differential equation (PDE) control of flexible manipulator. The proposed scheme considers the effects of boundary input force and gravity on the payload, which results in non-homogenous boundary conditions. This objective is achieved based on an appropriate model transformation scheme for homogenizing boundary conditions, which enables obtaining semi-analytical solutions for the corresponding PDE model. Model transformation is assigned as a hybrid exponential–polynomial function whose coefficients are conveniently calculable without the need for any additional boundary condition measurements. This results in elimination of the need for using intensive numerical solvers,  e.g., those based on finite element analysis, and allows for implementation of sophisticated PDE control methods considering fully nonlinear PDE models with high computation speed. Precision and efficiency of calculating distributed states using proposed model transformation is demonstrated based on experimental data for the manipulator with respect to ground truth camera-based motion capture system. The model transformation is also numerically implemented for the proposed nonlinear endpoint control method based on original PDE model. Note to practitioners—This paper investigates difficulty of obtaining data describing flexible manipulator pose required for precise control and analysis, and proposes a computationally efficient method to overcome this issue.

Upper-limb exoskeleton (ULE) arms have the potential to assist humans in accomplishing tasks by distributing a heavy load. ULE arms are designed to be comfortable and lightweight wearable robotic devices, a design that has resulted in the complexity of their structures, actuators, and power transmissions. Additionally, different ULE vendor structures and biomechanical variations between humans have resulted in dissimilar coordinated ULE arm systems. These complex multiple ULE arm systems can be handled through adaptive virtual decomposition control (VDC) if unknown dynamic models are not considered. Accordingly, this paper proposes a new distributed framework for the adaptive impedance-based VDC method to address the abovementioned challenges and thereby enhance the performance and robustness of the ULE arm systems. To that end, the proposed control method has a prediction capability and an ancillary control law for coordinated dissimilar ULE arms holding a common object. The system stability is analyzed using the input-to-state stability approach. The performance of the proposed controller is evaluated both in simulation with six coordinated ULE arms and in an experiment with two commercial coordinated ULE arms each with seven degrees of freedom. Four scenarios are performed with different internal arm forces with and without an obstacle. The simulation and experiment results are compared with a state-of-the-art adaptive VDC method and show the superiority of the proposed control method.