机器人系统建模与辨识工具箱sympybotic

Sympybotic是一款机器人运动学和动力学的符号推导工具包.

机器人参数辨识示意图

其主要依赖于两个工具包：

SymPy是用于符号数学的Python库。 它旨在组建功能齐全的计算机代数系统（CAS），同时保持代码尽可能的简单，以使其易于理解和易于扩展。 SymPy完全用Python编写。

安装方式具体如下所示

git clone https://github.com/cdsousa/SymPyBotics.git
cd sympybotics
python setup.py install           

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安装后可以通过如下代码测试系统功能

>>> import sympy
>>> import sympybotics
>>> rbtdef = sympybotics.RobotDef('Example Robot', # robot name
...                               [('-pi/2', 0, 0, 'q+pi/2'),  # list of tuples with Denavit-Hartenberg parameters
...                                ( 'pi/2', 0, 0, 'q-pi/2')], # (alpha, a, d, theta)
...                               dh_convention='standard' # either 'standard' or 'modified'
...                              )
>>> rbtdef.frictionmodel = {'Coulomb', 'viscous'} # options are None or a combination of 'Coulomb', 'viscous' and 'offset'
>>> rbtdef.gravityacc = sympy.Matrix([0.0, 0.0, -9.81]) # optional, this is the default value
 
rbt = sympybotics.RobotDynCode(rbtdef, verbose=True)
donerbt = sympybotics.RobotDynCode(rbtdef, verbose=True)
generating geometric model
generating kinematic model
generating inverse dynamics code
generating gravity term code
generating coriolis term code
generating coriolis matrix code
generating inertia matrix code
generating regressor matrix code
generating friction term code
done

>>> rbt.geo.T[-1]
Matrix([
[-sin(q1)*sin(q2), -cos(q1),  sin(q1)*cos(q2), 0],
[ sin(q2)*cos(q1), -sin(q1), -cos(q1)*cos(q2), 0],
[         cos(q2),        0,          sin(q2), 0],
[               0,        0,                0, 1]])

>>> tau_str = sympybotics.robotcodegen.robot_code_to_func('C', rbt.invdyn_code, 'tau_out', 'tau', rbtdef)

Doing print(tau_str), function code will be output:
void tau( double* tau_out, const double* parms, const double* q, const double* dq, const double* ddq )
{
  double x0 = sin(q[1]);
  double x1 = -dq[0];
  double x2 = -x1;
  double x3 = x0*x2;
  double x4 = cos(q[1]);
  double x5 = x2*x4;
  double x6 = parms[13]*x5 + parms[15]*dq[1] + parms[16]*x3;
  double x7 = parms[14]*x5 + parms[16]*dq[1] + parms[17]*x3;
  double x8 = -ddq[0];
  double x9 = -x4;
  double x10 = dq[1]*x1;
  double x11 = x0*x10 + x8*x9;
  double x12 = -x0*x8 - x10*x4;
  double x13 = 9.81*x0;
  double x14 = 9.81*x4;
  double x15 = parms[12]*x5 + parms[13]*dq[1] + parms[14]*x3;

  tau_out[0] = -parms[3]*x8 + x0*(parms[14]*x11 + parms[16]*ddq[1] + parms[17]*x12 - dq[1]*x15 - parms[19]*x14 + x5*x6) - x9*(parms[12]*x11 + parms[13]*ddq[1] + parms[14]*x12 + dq[1]*x7 + parms[19]*x13 - x3*x6);
  tau_out[1] = parms[13]*x11 + parms[15]*ddq[1] + parms[16]*x12 - parms[18]*x13 + parms[20]*x14 + x15*x3 - x5*x7;

  return;
}


Dynamic base parameters:
>>> rbt.calc_base_parms()
>>> rbt.dyn.baseparms
Matrix([
[L_1yy + L_2zz],
[         fv_1],
[         fc_1],
[L_2xx - L_2zz],
[        L_2xy],
[        L_2xz],
[        L_2yy],
[        L_2yz],
[         l_2x],
[         l_2z],
[         fv_2],
[         fc_2]])
           

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