This paper addresses the trajectory tracking problem for constrained high dynamic electrohydraulic actuator in the presence of time-varying parameters, high frequency external load interference, measurement noise and some unmeasurable states. An adaptive robust optimal control scheme is proposed for the electro-hydraulic actuator in legged robot. The framework of our presented scheme is based on a linear time-varying model predictive controller (LTV-MPC) embedded with a multi-scale online estimator (MEKF). With fast-varying and slow-varying time scales, the MEKF part is used not only for measurable states filtering and unmeasurable states estimation, but also for time-varying parameters and external load interference estimation, which will be integrated into the mpc model in real time. The LTV-MPC part is a trajectory tracking controller designed by constrained MPC with an approximate high-precision real-time model and a rapidly solved cost function, which guarantees that the input and output constraints are satisfied during the receding horizon and optimal control process. Finally, with a series of highly dynamic conditions, the comparison experiment results show that the proposed controller has a simple design process, strong adaptive robust performance and trajectory tracking performance, which verifies the effectiveness of the control scheme. INDEX TERMS Multi-scale online estimator, linear time-varying model predictive controller, electrohydraulic actuator.

Legged robots have extremely strong adaptability in different terrain environment and their stable walking in the wild is still a current research hotspot. Although they have shown great motion performance in recent years, most of them rely on high-performance sensors , especially force sensors settled on foot. However, it is impractical to select special forces sensors in the field environment, and the performance degradation and noise during the usage will bring fatal control defects. In order to solve this problem, we propose a foot contact force estimation method that does not require force sensors, and applies the estimated contact force to the impedance control of the legged robot to achieve the robot's active compliance control. The method of force estimation is based on the generalized momentum of the robot. It only needs to provide the position information of the joint and the information of the applied control torque. The designed feedforward and compensation terms effectively improve the speed and accuracy of the force estimation. We improved the response speed of the system to the contact force by improving the structure of the impedance control, and applied the estimated contact force to the impedance control to achieve the stable motion of the quadruped robot. Simulation experiments verify the effectiveness of the proposed force estimation method.

Aiming at the steady motion of the quadruped robot during support period of the locomotion, it is necessary to plan the ground reaction force (GRF) of legs. For the control of the plane height of the robot body, we take the standing balance of the simply modelled quadruped robot as the research object, and use the model predictive control algorithm to plan quadruped robot’s GRF of its position and attitude control, and then map the force to the operating space through the Jacobian matrix of the joint space to obtain the torque of the joint space. This paper uses MATLAB and RecurDyn for the co-simulation, and obtains good control results from it. At the end, we analyze the feasibility and rationality of its algorithm application by comparing it with the traditional balance controller. The work above provides the basis for the control and design of the subsequent quadruped robot motion planning.

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