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Hydraulic lower limb exoskeletons are wearable robotic systems, which can help people carry heavy loads. Recently, underactuated exoskeletons with some passive joints have been developed in large numbers for the purpose of decreasing the weight and energy consumption of the system. There are many control algorithms for a multi-joint fully actuated exoskeleton, which cannot be applied for underactuated systems due to the reduction in the number of control inputs. Besides, since the hydraulic actuator is not a desired force output source, there exist high order nonlinearities in hydraulic exoskeletons, which makes the controller design more challenging than motor driven exoskeleton systems. This paper proposed a precision interaction force controller for a 3DOF underactuated hydraulic stance leg exoskeleton. First, the control effect of the wearer is considered and the posture of the exoskeleton back is assumed as a desired trajectory under the control of the wearer. Under this assumption, the system dynamics are changed from a 3DOF underactuated system in joint space to a 2DOF fully actuated system in Cartesian space. Then, a three-level interaction force controller is designed in which the high-level controller conducts human motion intent inference, the middle level controller tracks human motion and the low-level controller achieves output force tracking of hydraulic cylinders. The MIMO adaptive robust control algorithm is applied in the controller design to effectively address the high order nonlinearities of the hydraulic system, multi-joint couplings and various model uncertainties. A gain tuning method is also provided to facilitate the controller gains selection for engineers. Comparative simulations are conducted, which demonstrate that the principal human-machine interaction force components can be minimized and good robust performance to load change and modeling errors can be achieved.

There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton's Principle, Kane's Equation. Compared to Newton-Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange's multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia-Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss's principle, d' Alembert's principle or extended d' Alembert's principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia-Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia-Kalaba Equation is given. Furthermore, the comparisons of Udwadia-Kalaba Equation with Newton-Euler Equation, Lagrange Equation and Kane's Equation are made, respectively. At last, three different types of examples are given for demonstrations.

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