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Compliant bipedal robots demonstrate a potential for impact resistance and high energy efficiency through the introduction of compliant elements. However, it also adds to the difficulty of stable control of the robot. To motivate the control strategies of compliant bipedal robots, this work presents an improved control strategy for the stable and fast planar jumping of a compliant one-legged robot designed by the authors, which utilizes the concept of the virtual pendulum. The robot was modeled as an extended spring-loaded inverted pendulum (SLIP) model with non-negligible torso inertia, leg inertia, and leg damping. To enable the robot to jump forward stably, a foot placement method was adopted, where due to the asymmetric feature of the extended SLIP model, a variable time coefficient and an integral term with respect to the forward speed tracking error were introduced to the method to accurately track a given forward speed. An energy-based leg rest length regulation method was used to compensate for the energy dissipation due to leg damping, where an integral term, regarding jumping height tracking error, was introduced to accurately track a given jumping height. Numerical simulations were conducted to validate the effectiveness of the proposed control strategy. Results show that stable and fast jumping of compliant one-legged robots could be achieved, and the desired forward speed and jumping height could also be accurately tracked. In addition to that, using the proposed control strategy, the robust jumping performance of the robot could be observed in the presence of disturbances from state variables or uneven terrain.

Purpose Hydrodynamic parameter estimation is significant for the velocity prediction of unmanned surface vehicles. Considering the field data’s uncertain nonlinearities (environmental disturbances and measurement noise), this paper aims to propose a hybrid adaptive parameter estimation (HAPE) strategy. Design/methodology/approach First, a rough estimation of hydrodynamic parameters is used by the least squares method. Second, an improved adaptive parameter estimation algorithm is applied to compensate for the influence of uncertain nonlinearities and adjust the parameters within the rough range. Finally, it is proved that the calculated velocity asymptotically converges to the actual value during the parameter estimation procedure. Findings The numerical simulation and pool experiments are conducted in two scenarios of steady turning and sinusoidal thrust to verify the effectiveness of the proposed HAPE method. The results validate that the accuracy of the predicted velocity using the hydrodynamic model obtained by the HAPE strategy is better than the APE algorithm. In addition, the hydrodynamic parameters estimated with the sinusoidal thrust data are more applicable than the steady turning data. Originality/value This study proposes a HAPE strategy that considers the uncertain nonlinearities of the field data. This method provides a more accurate predicted velocity. Besides, as far as we know, it is the first time to analyze the influence of different test conditions on the accuracy of the predicted velocity.