Tian Dingkui, Gao Junyao, Liu Chuzhao, Shi Xuanyang
School of Mechatronical Engineering, Intelligent Robotics Institute, Beijing Institute of Technology, Beijing 100081, China.
Sensors (Basel). 2021 Mar 8;21(5):1893. doi: 10.3390/s21051893.
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.
本文提出了一种基于二次规划（QP）的向上跳跃运动优化框架，该框架可以同时考虑诸如零力矩点（ZMP）、角加速度限制和防滑等约束条件。我们的方法包括两个部分：轨迹生成和实时控制。在起跳阶段的轨迹生成中，我们对连续轨迹进行离散化，并假设两个采样间隔之间的加速度是恒定的，然后将问题转化为一个非线性优化问题。在支撑阶段的实时控制中，诸如力矩中心（CoM）、角度和角动量跟踪等超约束控制目标，以及防滑、ZMP和关节加速度限制等约束条件，都统一在一个基于QP优化的框架内。通过简单的迭代即可获得驱动关节的输入角度。仿真结果表明，成功实现了向上跳跃至16.4厘米的高度，这证实了控制器完全满足所有约束条件并实现了控制目标。
