双足机器人简单步态生成

　　 让机器人行走最简单的方法是先得到一组步态曲线，即腿部每个关节随时间运动的角度值。可以在ADAMS或3D Max、Blender等软件中建立好机构/骨骼模型，设计出脚踝和髋关节的运动曲线，然后进行逆运动学解算，测量每个关节在运动过程中的转角，最后将得到的曲线导出。拿到曲线数据后我们就可以用单片机读取，然后发送给机器人的舵机去执行运行。这种方法的缺点是机器人只能按照固定的步态行走，不够灵活，比如抬脚高度、步长等参数都是定死的，如果需要修改还得再使用别的软件导出新的步态数据。

　　最简单的腿部结构如下图所示，在髋关节、膝关节和踝关节各有一个转动自由度，可以通过三角形余弦定理求得机构的运动学逆解。这种机器人只能在矢状面上直线前进，不能转弯。对行走过程进行一定的简化和假设：

1. 髋关节始终保持恒定的高度（实际上会有微小的波动）

2. 机器人脚面始终平行于地面

　　为了确定每个关节的角度，需要设计行走过程中踝关节点的运动轨迹。这里采用简单的正弦曲线作为其轨迹（也可以采用样条曲线、Bézier 曲线等），正弦曲线的幅值对应抬脚最大高度。

 

　　在Python中实现导入双腿模型文件，生成指定的步态数据后让其循环运动，就可以模拟机器人行走。代码如下（很糙...只是实现了基本功能，细节还有待完善）

#!/usr/bin/env python
import vtk
import math
from vtk.util.colors import *
import numpy as np
import time


actor  = list()   # the list of links
filenames = ["link-1.stl","link-2.stl","link-3.stl","link-4.stl","link-5.stl","link-6.stl"]
renWin = vtk.vtkRenderWindow()

joint1 = vtk.vtkAssembly()
joint2 = vtk.vtkAssembly()
joint3 = vtk.vtkAssembly()
joint4 = vtk.vtkAssembly()
joint5 = vtk.vtkAssembly()
joint6 = vtk.vtkAssembly()

ThighLength = 100.0
ShankLength = 100.0
HipHeight = 180.0
FootLift = 10
StrideLength = 60
Subdivision = 20

leg_joint = np.zeros(3, dtype=np.float)
patterns = np.zeros((2*Subdivision ,6), dtype=np.float)
_p = 0

txt = vtk.vtkTextActor()
distance = 0.0


def Rad2Deg(rad):
    return  rad * 180.0 / math.pi


def FootHeight(x): 
    return (HipHeight - FootLift * math.cos(abs(x * math.pi / StrideLength)))


def LegIK(x, y):
    global leg_joint
    dist = math.sqrt(x**2 + y**2)
    leg_joint[0] = math.acos(dist / (2 * ShankLength)) + math.atan2(x, y)
    leg_joint[1] = math.pi - math.acos((ThighLength**2 + ShankLength**2 - dist**2) / (2 * ThighLength* ShankLength))
    leg_joint[2] = leg_joint[1] - leg_joint[0]


def GenerateGait():
    global leg_joint
    global patterns

    # Move left leg forward.  
    for i in range(Subdivision):
        x = (i - Subdivision/2) * (StrideLength / Subdivision)
        y = FootHeight(x)        
        LegIK(x, y)            
        patterns[i, :3] = Rad2Deg(leg_joint)

    # Move left leg backward.  
    for i in range(Subdivision):
        x = (Subdivision/2 - i) * (StrideLength / Subdivision)
        y = HipHeight
        LegIK(x, y)                
        patterns[i+Subdivision, :3] = Rad2Deg(leg_joint)  

    # Build right leg from phase shift clone of left. 
    for i in range(2*Subdivision):
        patterns[i, 3:] = -patterns[(i + Subdivision) % (2*Subdivision), :3]


 
# Customize vtkInteractorStyleTrackballCamera 
class MyInteractor(vtk.vtkInteractorStyleTrackballCamera):
    def __init__(self,parent=None):
        self.AddObserver("CharEvent",self.OnCharEvent)
        self.AddObserver("KeyPressEvent",self.OnKeyPressEvent)

    def OnCharEvent(self,obj,event):
        pass
    
    def OnKeyPressEvent(self,obj,event):
        global _p
        global distance
        
        # Get the compound key strokes for the event
        key = self.GetInteractor().GetKeySym()
        
        GenerateGait()

        if(key == "Return"):
            # start animation
            joint1.SetPosition(0, 0, HipHeight-ThighLength-ShankLength)
            joint4.SetPosition(0, 0, HipHeight-ThighLength-ShankLength)
            
            if (_p == 2*Subdivision):
                _p = 0
     
            joint1.SetOrientation(0, -patterns[_p][0], 0)
            joint2.SetOrientation(0, patterns[_p][1], 0)
            joint3.SetOrientation(0, -patterns[_p][2], 0)

            joint4.SetOrientation(0, patterns[_p][3], 0)
            joint5.SetOrientation(0, -patterns[_p][4], 0)
            joint6.SetOrientation(0, patterns[_p][5], 0)

            _p = _p + 1

            distance = distance + StrideLength/(2 * Subdivision * 1000.0)
            txt.SetInput("Distance: " + str(distance) + "m")
            
            renWin.Render()
                
        return
    


def CreateCoordinates():
    # create coordinate axes in the render window
    axes = vtk.vtkAxesActor() 
    axes.SetTotalLength(40, 40, 40)  # Set the total length of the axes in 3 dimensions 

    # Set the type of the shaft to a cylinder:0, line:1, or user defined geometry. 
    axes.SetShaftType(0) 

    transform = vtk.vtkTransform() 
    transform.Translate(0.0, 0.0, 200.0)
    axes.SetUserTransform(transform)

    axes.SetCylinderRadius(0.02) 
    axes.GetXAxisCaptionActor2D().SetWidth(0.03) 
    axes.GetYAxisCaptionActor2D().SetWidth(0.03) 
    axes.GetZAxisCaptionActor2D().SetWidth(0.03) 
    return axes


def CreateGround():
    # create plane source
    plane = vtk.vtkPlaneSource()
    plane.SetXResolution(20)
    plane.SetYResolution(20)
    plane.SetCenter(0,0,0)
    plane.SetNormal(0,0,1)

    # mapper
    mapper = vtk.vtkPolyDataMapper()
    mapper.SetInputConnection(plane.GetOutputPort())

    # actor
    actor = vtk.vtkActor()
    actor.SetMapper(mapper)
    actor.GetProperty().SetRepresentationToWireframe()
    actor.GetProperty().SetColor(light_grey)

    transform = vtk.vtkTransform()
    transform.Scale(400,400,1)
    actor.SetUserTransform(transform)

    return actor
    

def LoadSTL(filename):
    reader = vtk.vtkSTLReader()
    reader.SetFileName(filename)
    mapper = vtk.vtkPolyDataMapper() # maps polygonal data to graphics primitives
    mapper.SetInputConnection(reader.GetOutputPort())
    actor = vtk.vtkLODActor() 
    actor.SetMapper(mapper)
    return actor   # represents an entity in a rendered scene

            
def CreateScene():
    # Create a rendering window and renderer
    ren = vtk.vtkRenderer()
    renWin.AddRenderer(ren)
     
    # Create a renderwindowinteractor
    iren = vtk.vtkRenderWindowInteractor()
    iren.SetRenderWindow(renWin)
    style = MyInteractor()
    style.SetDefaultRenderer(ren)
    iren.SetInteractorStyle(style)
    
    for id, file in enumerate(filenames):
        actor.append(LoadSTL(file))
        r = vtk.vtkMath.Random(.4, 1.0)
        g = vtk.vtkMath.Random(.4, 1.0)
        b = vtk.vtkMath.Random(.4, 1.0)
        actor[id].GetProperty().SetDiffuseColor(r, g, b)
        actor[id].GetProperty().SetDiffuse(.8)
        actor[id].GetProperty().SetSpecular(.5)
        actor[id].GetProperty().SetSpecularColor(1.0,1.0,1.0)
        actor[id].GetProperty().SetSpecularPower(30.0)

    joint1.AddPart(actor[0])
    joint1.AddPart(joint2)
    joint2.AddPart(actor[1])
    joint2.AddPart(joint3)
    joint3.AddPart(actor[2])

    joint4.AddPart(actor[3])
    joint4.AddPart(joint5)
    joint5.AddPart(actor[4])
    joint5.AddPart(joint6)
    joint6.AddPart(actor[5])
    
    joint1.SetOrigin(0, 0, 200)
    joint4.SetOrigin(0, 0, 200)
    joint2.SetOrigin(0, 0, 100)
    joint5.SetOrigin(0, 0, 100)

    ren.AddActor(joint1)
    ren.AddActor(joint4)

    # Add coordinates
    axes = CreateCoordinates()
    ren.AddActor(axes)

    # Add ground
    ground = CreateGround()
    ren.AddActor(ground)

    # create a text actor
    txt.SetInput("Distance: 0m")
    txtprop=txt.GetTextProperty()
    txtprop.SetFontFamilyToArial()
    txtprop.SetFontSize(18)
    txtprop.SetColor(1,1,1)
    txt.SetDisplayPosition(450,550)
        
    # assign actor to the renderer
    ren.AddActor(txt)

    # Set background color
    ren.SetBackground(.1, .1, .1)

    # Set window size
    renWin.SetSize(600, 600)

    # Enable user interface interactor
    iren.Initialize()
    iren.Start()
    
    
if __name__ == "__main__":
    CreateScene()

　　按住回车键，一帧一帧播放动画。最后的效果是这样的:

 

参考：

https://github.com/Rhoban/IKWalk

Using Inverse Kinematics to Develop a Biped Robot Walking Gait C#

8 DOF Biped Robot using Dynamixel AX-12A Servos and Arduino