人形机器人是外表与人类相似的高端智能设备，其机械结构模拟人类身体构造，拥有强大的运动能力，能够快速适应人类环境和使用为人类使用的工具，是我国未来智能产业的重要领域之一。当前，对人形机器人行走、跑步等运动状态的研究已取得较大进展，而对于跳跃运动的研究尚不成熟，从而限制了人形机器人处理障碍、沟壑等有垂直高度变化的非结构化环境的能力。为提升人形机器人复杂环境适应能力，本文针对人形机器人跳跃运动的动作规划与控制策略展开了研究，主要研究内容和成果如下： （1）针对人形机器人跳跃运动进行分析，基于浮动基坐标建立人形机器人跳跃运动的数学模型。根据人形机器人的关节自由度以及机械结构几何参数，推导了人形机器人各关节坐标系的齐次变换矩阵。基于人形机器人广义关节坐标系之间的递推关系，建立了人形机器人的运动学模型和浮动基动力学模型。 （2）基于高斯伪谱法实现对人形机器人简化模型的跳跃运动进行离线规划。通过对人形机器人跳跃运动分析，可以将连续时间优化问题通过全局插值近似进行离散化，采用高斯伪谱法求得离散非线性最优问题的解析解，作为机器人跳跃运动的最优轨迹。 （3）基于微分动态规划算法实现对人形机器人全模型跳跃运动进行离线规划。利用Crocoddyl库提供的微分动态规划算法，通过灵活的动力学建模和高效的轨迹优化，实现对人形机器人跳跃运动的全身轨迹优化。与高斯伪谱法相比，Crocoddyl库不仅能够处理高维度和复杂系统，更具备较高的计算效率和快速求解能力。 （4）提出了基于二次优化的全身动力学权重优化控制策略。针对机器人运动过程中目标的多样性和机体本身的多自由度，将机器人跳跃控制任务分解为多目标优化任务并设计不同权重，并设计各任务跟踪PD反馈控制器，根据人形机器人跳跃运动过程中的不同阶段自由修改约束条件，各阶段不同的控制任务和约束条件共同构成统一的二次规划求解框架，从而实现了在仿真环境中机器人向前跳跃0.5米的运动，验证了该控制方法的有效性。
Humanoid robots are advanced intelligent devices designed to resemble humans in appearance, with mechanical structures that is similar to the human body. They possess robust mobility and the ability to rapidly adapt to human environments and utilize tools designed for human use. As such, they represent one of the critical domains in the future of intelligent industries in our country. While significant progress has been made in studying motion states such as standing, walking and running, research on jumping motion remains underdeveloped, limiting the ability of humanoid robots to navigate environments with vertical height variations, such as obstacles and ditches. To improve the complex environment adaptability of humanoid robot, this paper investigates the motion planning and control strategy of humanoid robot jumping motion. The main research contents and results are as follows: (1)Mathematical modeling and analysis of humanoid jumping dynamics. Firstly, the joint parameters and degrees of freedom of the humanoid robot are configured, and the whole body coordinate system of the human robot based on the floating coordinate system is established. Secondly, based on the structural parameters of the humanoid robot, the floating base kinematic equations and the robot joint coordinate systems are derived. Finally, by using the Lagrange method, the dynamics of the jumping motion of the humanoid robot is derived. (2) Offline planning of jumping motion for a simplified humanoid robot model using the Gauss pseudospectral method. By analyzing the jumping motion of the humanoid robot, the continuous-time optimization problem is discretized through global interpolation approximation. The Gauss pseudospectral method is employed to obtain the analytical solution of the discrete nonlinear optimization problem, which serves as the optimal trajectory for the robot's jumping motion. (3) Offline planning of jumping motion for the full humanoid robot model using the differential dynamic programming algorithm. The differential dynamic programming algorithm provided by the Crocoddyl library is utilized to achieve whole-body trajectory optimization for the humanoid robot's jumping motion through flexible dynamics modeling and efficient trajectory optimization. Compared to the Gauss pseudospectral method, the Crocoddyl library not only handles high-dimensional and complex systems but also exhibits higher computational efficiency and rapid solving capabilities. (4) Weight-Optimized quadratic programming-based control strategy for whole-body jumping dynamics. This strategy addresses the multi-objective nature of robotic jumping by decomposing control tasks into weighted subtasks with prioritized objectives. A PD feedback controllers are designed for each task to track and modify constraints freely according to different stages of the humanoid robot jumping process. The different control tasks and constraints in each stage together form a unified quadratic programming (QP) framework. Simulations validate the method’s efficacy, demonstrating a 0.5-meter forward jump, thereby confirming the robustness of the proposed control strategy.
