Highly dynamic movements such as jumping are important to improve the agility and environmental adaptation of humanoid robots. This article proposes an online optimization method to realize a vertical jump with centroidal angular momentum (CAM) control and landing impact absorption for a humanoid robot. First, the robot's center of mass (CoM) trajectory is generated by nonlinear optimization. Then, a quasi-sliding mode controller is designed to ensure that the robot tracks the CoM trajectory accurately. To avoid unexpected spinning in the flight phase, a center-of-pressure-guided angular momentum controller is designed to stabilize the CAM. The modifications of CoM and CAM are realized by online optimization of dynamic components and inverse dynamics. Two quadratic programming optimizations are utilized to generate feasible contact force/torque and joint acceleration referring to uplevel CoM and CAM controllers. In addition, a viscoelastic model-based controller is designed to absorb the vibration caused by a large contact impact. A simulation and experiment of a 0.5-m high (foot lifting distance) vertical jump are achieved on a humanoid robot platform in this article (Fig. 1).

High vertical jumping motion, which enables a humanoid robot to leap over obstacles, is a direct reflection of its extreme motion capabilities. This article proposes a single sequential kino-dynamic trajectory optimization method to solve the whole-body motion trajectory for high vertical jumping motion. The trajectory optimization process is decomposed into two sequential optimization parts: optimization computation of centroidal dynamics and coherent whole-body kinematics. Both optimization problems converge on the common variables (the center of mass, momentum, and foot position) using cost functions while allowing for some tolerance in the consistency of the foot position. Additionally, complementarity conditions and a pre-defined contact sequence are implemented to constrain the contact force and foot position during the launching and flight phases. The whole-body trajectory, including the launching and flight phases, can be efficiently solved by a single sequential optimization, which is an efficient solution for the vertical jumping motion. Finally, the whole-body trajectory generated by the proposed optimized method is demonstrated on a real humanoid robot platform, and a vertical jumping motion of 0.5 m in height (foot lifting distance) is achieved.

High dynamic jump motions are challenging tasks for humanoid robots to achieve environment adaptation and obstacle crossing. The trajectory optimization is a practical method to achieve high-dynamic and explosive jumping. This paper proposes a 3-step trajectory optimization framework for generating a jump motion for a humanoid robot. To improve iteration speed and achieve ideal performance, the framework comprises three sub-optimizations. The first optimization incorporates momentum, inertia, and center of pressure (CoP), treating the robot as a static reaction momentum pendulum (SRMP) model to generate corresponding trajectories. The second optimization maps these trajectories to joint space using effective Quadratic Programming (QP) solvers. Finally, the third optimization generates whole-body joint trajectories utilizing trajectories generated by previous parts. With the combined consideration of momentum and inertia, the robot achieves agile forward jump motions. A simulation and experiments (Fig. \ref{Fig First page fig}) of forward jump with a distance of 1.0 m and 0.5 m height are presented in this paper, validating the applicability of the proposed framework.

A kind of closed hydraulic system controlled by servo motor and constant pump is introduced for controlling the experimental press. By using AMESim and Adams, the hydraulic system model and motion model of the beam of the experimental press are established and co-simulation is carried out. PID controller is used in this hydraulic system to improve the control performance. Simulation results indicate that the position, speed and pressure control of the hydraulic system can meet the design requirements, providing a theoretic basis for the design and debugging of hydraulic system of the actual press.