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.

This article proposes an active disturbance rejection controller design scheme to stabilize the unstable limit cycle of a compass-like biped robot. The idea of transverse coordinate transformation is applied to form the control system based on angular momentum. With the linearization approximation, the limit cycle stabilization problem is simplified into the stabilization of an linear time-invariant system, which is known as transverse coordinate control. In order to solve the problem of poor adaptability caused by linearization approximation, we design an active disturbance rejection controller in the form of a serial system. With the active disturbance rejection controller, the system error can be estimated by extended state observer and compensated by nonlinear state error feedback, and the unstable limit cycle can be stabilized. The numerical simulations show that the control law enhances the performance of transverse coordinate control.

Biped robots’ locomotion is realized by driving the joint motion via a drive chain. Therefore, the stiffness of the drive chain is an important factor that affects the drive performance and can influence the locomotion behavior of the biped robot. This work focused on the influence of the stiffness of the leg’s drive chain using a mass-spring model based on the biped robot AIRO built in Zhejiang Lab. Methods for determination of the parameters in the proposed model were presented, including the use of ANSYS Workbench to determine the stiffness parameters and the determination of the inertia parameters by dynamic modelling of the biped robot. Simulation results show that special attention should be paid to the stiffness of the drive train of the leg when designing a biped robot to ensure the walking capability of the robot. Using the model proposed in this work, relations between the executed accuracy of the joint trajectories and the stiffness can be analyzed; after that, the stiffness parameters can be optimized. In addition, simulation results also showed that attention should be paid to manufacturing tolerances to ensure the symmetry of the legs of the bipedal robot in order to reduce the vibration of the robot body. Experiments were conducted on AIRO for validating the proposed model and the simulation analysis.