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Model-based force control for motion and force tracking faces significant challenges on real quadruped platforms due to the apparent model inaccuracies. In this paper, we present a multi-objective optimal torque control for hydraulic quadruped robots under significant model errors, such as non-modelable hydraulic components, linearization, disturbances, etc. More specifically, the centroidal dynamics are first modeled to project the dynamics of the floating-based whole-body behaviors to the centroidal frame. Model error compensation mechanisms are subsequently developed to track the reference motion of the CoM, torso, and foot-end trajectories, which are mapped into the joint space. Furthermore, a multi-objective optimal torque control scheme is formulated using quadratic programming (QP) to coordinate follow the reference motion and ground reaction forces simultaneously while satisfying all constraints. Finally, we present a series of simulations as well as experiments on a real hydraulic quadruped platform, EHbot. The results demonstrate that the proposed torque control scheme is robust to large model inaccuracies and improves the performance of the overall system.

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With the advent of force control in legged robots, there is an increasing demand in research on controlling contact forces that can ensure stable interaction and balance of the system. This article aims to solve the force distribution problem by an analytic solution to regulate the contact forces particularly in a computationally efficient manner. To this end, compliance models, consisting of a virtual model of the torso and impedance models of supporting feet, are developed for a quadruped robot. The linear constraints are formulated for the analytic method based on the compliance models, and the minimization of foot slippage and the internal forces within the closed chain are also taken into account. Moreover, given the compliance models, the postural compensation of the torso can be achieved by modifying the trajectories of supporting feet in order to generate desired forces. The comparisons between the proposed analytic and numerical methods show that the analytic one is advantageous for embedded controllers due to its high computational efficiency. Finally, the effectiveness of the proposed method is first validated in simulations and then in experiments on a physical quadruped robot, and the data are presented and analyzed.

This article presents a mechanical design structure for hydraulic actuators using the principle of series-elastic actuator, considering the restriction of mechanical structure, weight and size, as well as the requirement of high joint torques due to the large payload. An articulated leg was designed to incorporate with two of these elastic elements symmetrically for each joint. Further, for the hydraulic system with a position servo loop, a force control algorithm was particularly proposed and developed for joint torque tracking and Cartesian impedance control. Finally, a number of experiments were carried out on the leg platform, and the experimental results validated the effectiveness of the force control algorithm and the performance of the overall system.