Biosbot [20-21] CPG [22] 2 CPG Modeling of CPG 8 CPG 8 CPG 1 L R F H H K 4 4 φ i, i = 1,2,3,4 φ k CPG (1) θ A T CPG r h k 1 Tab Fig.1 C

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1 ROBOT Vol.33, No.6 Nov., 2011 DOI /SP.J TP24 A (2011) Quadruped Robot Walking Control on Trench-like Noncontinuous Terrain ZENG Xiangyu E Mingcheng LI Dongdong ZHANG Xiuli (School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing , China) Abstract: For the problem that a quadruped robot loses its balance when walking into a trench in the fields or on a downward non-structured step, a balance control solution, aiming at counteracting the vertical inertial force is proposed, based on the biological neural reflex mechanism. The detected abrupt change of the body pitch angle will trigger the postural reflex, which will produce coordinated movements of the four legs to adjust the robot s attitude rapidly to counteract instantaneous imbalance caused by inertia. Physical experiments are designed comparatively using a 8-DOF quadruped robot. The robot successfully crosses over a 1.2-leg-stride wide trench and walks down a 0.4-leg-length high step. Keywords: quadruped robot; central pattern generator; rough terrain; loss-foothold reflex; anti-inertia 1 Introduction BigDog [1-3] BigDog [4] BigDog BigDog Little Dog [5-9] Ijspeert [10] Kimura [11] Fukuoka [12] CPG [13-15] Kimura Tekken [16-18] 0.6 m/s 0.8 m/s Takemura TITAN [19] JBM089 zhangxl@bjtu.edu.cn / /

2 Biosbot [20-21] CPG [22] 2 CPG Modeling of CPG 8 CPG 8 CPG 1 L R F H H K 4 4 φ i, i = 1,2,3,4 φ k CPG (1) θ A T CPG r h k 1 Tab Fig.1 CPG CPG model Definitions and values of the parameters θ A CPG 12 T CPG 2 s [ ] 0, π, 0, π Φ φ k π/2 F k 0 1 θ 0 25 n 4 Θ s A s T s t s s F s 0 1 φ s Θ i Θ(t) = [ θ h,i (t), θ k,i (t) ] Φ = [ ] φ i i = 1,2,3,4 0.36π [ 0, 40, 30, 50 ] (1)

3 θ h,i (t) = A h sin(2πt/t + φ i ) A k sin(2πt/t + φ i + φ k ), F k = 0 θ k,i (t) = max(0,a k sin(2πt/t + φ i + φ k )), F k = 1 3 Modeling of loss-foothold reflex ZMP (2) ˆΘ(t) = Θ(t) + F s Θ s (t) Θ s (t) = [ θ s,h,i (t), θ s,k,i (t) ] (2) i = 1,2,3,4 θ s,h,i (t) = A s sin((2π(t mod T ) φ s )/T s ) θ s,k,i (t) = A s sin((2π(t mod T ) φ s )/T s ) Θ(t) Θ s (t) s 3 Fig.2 2 The schematic of loss-foothold reflex over a trench 3.2 Fig.3 3 The planning trajectories of loss-foothold reflex over a trench

第 33 卷第 6 期曾翔宇等沟壑类非连续地形下的四足机器人运动控制可确定机器人后腿已下台阶此时机器人恢复原来的节律运动进入平地行走状态反射建模台阶地形采用踏空调整反射由 4 条腿协调运动共同完成如图 4 首先通过踏空跨步 Fig.

修改机器人节律运动的平衡位置同时膝关节切换为半波模型表 1 中 Fk = 1 来实现踏空调整反射模型如下 Θ Θ (t) = Θ (t) + FsΘ s (t) + FiΘ i (t) (3) Θ i (t) = Θi 其中 Θ i (t) 为叠加的姿势调整模型 Θi 为常数矩阵 Fi 为触发开关下标 i 表示台阶地形踏空反射 4 图 5 四足机器人

1 四足机器人 Biosbot-V 四足机器人 Biosbot-V 图 5 由躯干和 4 条结构完全相同的腿组成躯干为工字梁造型每条腿有髋膝 2 个主动关节由直流电机通过配装的齿轮减速器直接驱动足为半圆形底部粘有防滑橡胶躯干和腿通过螺栓连接形成吊装结构横梁及纵梁上均开有多组吊装孔可以改变腿的安装位置从而改变横向及纵向腿距每个关节有 1

4 第 33 卷第 6 期曾翔宇等沟壑类非连续地形下的四足机器人运动控制可确定机器人后腿已下台阶此时机器人恢复原来的节律运动进入平地行走状态反射建模台阶地形采用踏空调整反射由 4 条腿协调运动共同完成如图 4 首先通过踏空跨步 Fig 反射使两条前腿前伸扩大稳定域同时使两条后腿下蹲调整躯体姿态呈大致水平以此减小垂直惯性力造成的冲击然后按原节律运动使两条后腿走下台阶同时恢复至原来姿态图 4 台阶地形踏空反射示意图 The schematic of loss-foothold reflex over a step 姿势调整通过给每一个关节角叠加一个恒定的角度值修改机器人节律运动的平衡位置同时膝关节切换为半波模型表 1 中 Fk = 1 来实现踏空调整反射模型如下 Θ Θ (t) = Θ (t) + FsΘ s (t) + FiΘ i (t) (3) Θ i (t) = Θi 其中 Θ i (t) 为叠加的姿势调整模型 Θi 为常数矩阵 Fi 为触发开关下标 i 表示台阶地形踏空反射 4 图 5 四足机器人 Biosbot-V Fig.5 The quadruped robot Biosbot-V 实验 Experiments 4.1 四足机器人 Biosbot-V 四足机器人 Biosbot-V 图 5 由躯干和 4 条结构完全相同的腿组成躯干为工字梁造型每条腿有髋膝 2 个主动关节由直流电机通过配装的齿轮减速器直接驱动足为半圆形底部粘有防滑橡胶躯干和腿通过螺栓连接形成吊装结构横梁及纵梁上均开有多组吊装孔可以改变腿的安装位置从而改变横向及纵向腿距每个关节有 1 个俯仰自由度机器人共 8 个自由度所有关节均可摆动近 180 机器人几何尺寸为 400 mm 320 mm 280 mm 质量为 5 kg 4.2 沟壑地形踏空反射实验添加踏空跨步反射的运动实验曲线如图 6 可以看出左前腿在约 2.6 s 处发生了踏空反射与前文中规划的踏空反射曲线基本一致图 7 为实验录像截图机器人在图 7(c) 帧处发生反射踏空腿的髋膝关节迅速前摆并落下成功通过沟壑 Fig.6 图 6 沟壑地形踏空反射实验曲线 The experimental motion profile of the loss-foothold reflex over a trench 图 7 沟壑地形踏空反射实验截图左前腿 Fig.7 The experimental images of loss-foothold reflex over a trench (front left leg)

704 机器人 2011 年 11 月 4.3 台阶地形踏空反射实验加入踏空调整反射的实验数据如图 8 为各关节运动轨迹及俯仰方向倾角计的信息图 9 为视频截图可以看出左前腿和右前腿分别在 4.5 s 和 5.5 s 的时刻踏空根据俯仰方向倾角计的信息在 4.

4 对比实验不加入反射模型的对比实验中面对沟壑地形机器人踏入沟壑侧翻面对台阶地形机器人或侧翻或重心前倾足部在台阶上打滑停滞不前引入两种踏空反射模型后机器人成功跨越沟壑完成下台阶动作经多次实验测得机器人最大可跨越沟壑宽度为 1.2 个跨距 80 mm 相当于 0.

台阶建立了踏空调整反射模型设计了反射的触发参考文献 References 结束条件以及与节律运动的相互融合机制最后以 [1] 四足机器人 Biosbot-V 为平台进行了对比实验成功实现了跨越 1.2 倍跨距的沟壑和走下 0.

5 704 机器人 2011 年 11 月 4.3 台阶地形踏空反射实验加入踏空调整反射的实验数据如图 8 为各关节运动轨迹及俯仰方向倾角计的信息图 9 为视频截图可以看出左前腿和右前腿分别在 4.5 s 和 5.5 s 的时刻踏空根据俯仰方向倾角计的信息在 4.7 s 时刻倾角计角度值超限触发姿势调整机器人后腿屈曲前腿伸直调整姿势后走下台阶在 8.8 s 时刻倾角计角度值恢复正常值表示完成下台阶动作机器人回归正常节律运动 4.4 对比实验不加入反射模型的对比实验中面对沟壑地形机器人踏入沟壑侧翻面对台阶地形机器人或侧翻或重心前倾足部在台阶上打滑停滞不前引入两种踏空反射模型后机器人成功跨越沟壑完成下台阶动作经多次实验测得机器人最大可跨越沟壑宽度为 1.2 个跨距 80 mm 相当于 0.3 个腿长下台阶高度为 100 mm 相当于 0.4 个腿长 5 结论 Conclusion 本文针对四足仿生机器人面临野外沟壑或非结构化台阶等未知突变地形时出现的姿态失稳问题提出模仿生物神经反射机理的抗垂直惯性力平衡控 Fig.8 图 8 台阶地形踏空反射实验曲线 The experimental motion profile of the loss-foothold reflex on a step 图 9 台阶地形踏空反射实验截图 Fig.9 The experimental images of loss-foothold reflex on a step 制方法文中建立了 CPG 模型用于实现基本节律运建立复杂的环境模型可以对未知地形做出快速反动针对沟壑地形建立了踏空跨步反射模型针对应有望应用于军事救援星球探测等特殊领域台阶建立了踏空调整反射模型设计了反射的触发参考文献 References 结束条件以及与节律运动的相互融合机制最后以 [1] 四足机器人 Biosbot-V 为平台进行了对比实验成功实现了跨越 1.2 倍跨距的沟壑和走下 0.4 倍腿长的台阶本文提出的突变地形抗垂直惯性力平衡控制方法利用反射机制产生运动的适应性不需要 [2] Raibert M, Blankespoor K, Nelson G, et al. BigDog, the roughterrain quadruped robot[c]//proceedings of the 17th World Congress, The International Federation of Automatic Control Wooden D, Malchano M, Blankespoor K, et al. Autonomous navigation for BigDog[C]//IEEE International Conference on

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第 48 卷第 6 期 2 1 6 年 6 月哈尔滨工业大学学报 JOURNAL OF HARBIN INSTITUTE OF TECHNOLOGY Vol 48 No 6 Jun. 216 doi:1.11918 / j.issn.367 6234.216.6.1 大跨度楼盖结构在运动荷载下的振动性能杨维国 1, 马伯涛 2, 宋毛