Abstract
An optimization framework for upward jumping motion based on quadratic programming (QP) is proposed in this paper, which can simultaneously consider constraints such as the zero moment point (ZMP), limitation of angular accelerations, and anti-slippage. Our approach comprises two parts: the trajectory generation and real-time control. In the trajectory generation for the launch phase, we discretize the continuous trajectories and assume that the accelerations between the two sampling intervals are constant and transcribe the problem into a nonlinear optimization problem. In the real-time control of the stance phase, the over-constrained control objectives such as the tracking of the center of moment (CoM), angle, and angular momentum, and constraints such as the anti-slippage, ZMP, and limitation of joint acceleration are unified within a framework based on QP optimization. Input angles of the actuated joints are thus obtained through a simple iteration. The simulation result reveals that a successful upward jump to a height of 16.4 cm was achieved, which confirms that the controller fully satisfies all constraints and achieves the control objectives.
Highlights
Jumping enables more flexibility and stronger terrain adaptability for robots in unstructured terrain
Because this study focused on upward jumping, the center of moment (CoM) position does not change in the horizontal direction, and the following relationships hold:
In the trajectory generation of the robot’s flight phase, it is considered that the robot is only subjected to gravity in the vertical direction, the linear momentum is in the horizontal direction, and the angular momentum with the CoM is conserved
Summary
Jumping enables more flexibility and stronger terrain adaptability for robots in unstructured terrain. Barkan and Kajita prevented the robot from falling down by performing ZMP tracking for the desired trajectories instead of only constraining the ZMP inside the support polygon, but their algorithm has poor scalability and compatibility This means that it is difficult to add various constraints, which should have been considered but were ignored in this scheme, such as the anti-slippage and limitation of the angle and angular accelerations, or add other tasks such as joint tracking. There are 4 control goals but only 3 control variables, i.e., the actuated joints’ accelerations, which leads us to unify this over-constrained jumping problem into a framework based on QP optimization with different weights and many constraints. In the real-time control of the flight phase, we only execute the planned angle of the actuated joints
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