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摘要: 欠驱动双足机器人在行走中为保持自身的平衡, 双脚需要不间断运动. 但在仅有特定立足点的离散地形上很难实现调整后的落脚点, 从而导致欠驱动双足机器人在复杂环境中的适应能力下降. 提出了基于虚拟约束(Virtual constraint, VC)的变步长调节与控制方法, 根据欠驱动双足机器人当前状态与参考落脚点设计了非时变尺度缩放因子, 能够实时重构适应当前环境的步态轨迹; 同时构建了全身动力学模型, 采用反馈线性化的模型预测控制 (Model predictive control, MPC) 滚动优化产生力矩控制量, 实现准确的轨迹跟踪控制. 最终进行了欠驱动双足机器人的随机离散地形稳定行走的仿真实验, 验证了所提方法的有效性与鲁棒性.Abstract: To keep the balance of the underactuated biped robot during walking, its feet need to move continuously. However, it is difficult to achieve the adjusted foothold on the discrete terrain with only a specific foothold, which decreases the adaptability of underactuated biped robots in complex environments. This paper proposes a variable step-size adjustment and control method based on virtual constraints (VC). Time-invariant scaling factors are designed according to the underactuated biped robot＇s current state and reference point, which can reconstruct the gait trajectory by adapting to the current environment in real-time. Meanwhile, the whole body dynamics model is constructed. The torque control is generated by rolling optimization using model predictive control (MPC) with feedback linearization to achieve accurate trajectory tracking control. Finally, an underactuated biped robot walking stably on random discrete terrain is simulated to verify the effectiveness and robustness of the proposed method.
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图 6 机器人平地固定步长行走仿真截图
Fig. 6 Simulation screenshot of robot walking with fixed step length on flat ground
图 8 机器人单脚支撑期的关节驱动力矩
Fig. 8 Joint driving torque of robot during one leg support period
图 10 机器人变步长离散地形行走仿真截图
Fig. 10 Simulation screenshot of robot walking on discrete terrain with variable step-size
图 11 离散平地变步长运动中的尺度因子与VC轨迹变化
Fig. 11 Scale factor and VC trajectory variation in discrete flat variable step-size motion
图 12 离散平地变步长行走的步长误差
Fig. 12 Step error of discrete variable step-size walking on flat ground
图 13 随机离散变步长变高度行走的仿真截图
Fig. 13 Simulation screenshot of random discrete variable step-size and variable height walking
图 14 空间中参考落脚点与实际落脚点的示意图
Fig. 14 Schematic diagram of reference foothold and actual foothold in space
图 15 随机离散地形运行中的尺度缩放因子和VC参考轨迹
Fig. 15 Scaling factor and VC reference trajectory in random discrete terrain
图 17 机器人行走受扰动后的尺度因子变化情况
Fig. 17 The change of scale factor after the robot is disturbed in walking
图 18 机器人行走中有无扰动下躯干姿态变化
Fig. 18 The posture change of the trunk with or without disturbance during robot walking
表 1 仿真参数设置
Table 1 Parameters setting in simulation
参数 取值 单位 上身目标角度$\alpha _{\text{tor}}^{\text{ref}}$ 0 rad 固定步长${L_{\text{step}}}$ 0.4 m 最大抬腿量${}^{\max }z_{\text{foot}}^{\text{ref}}$ 0.1 m 调节量$\sigma $ 0.1 m 髋关节最大高度$Z_{\text{hip}}^{\max }$ 0.7 m 髋关节最小高度$Z_{\text{hip}}^{\min }$ 0.6 m 控制周期为$\Delta T$ 0.001 s 预测步长$NP$ 5 步 状态权重系数 0.1 − 控制权重系数 0.001 − 驱动力矩边界值${u_{\min }}$ −200 N·m 驱动力矩边界值${u_{\max }}$ 200 N·m 
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