Modified DH notation robot class. More...

#include <robot.h>

Inheritance diagram for mRobot:

Public Member Functions
virtual ReturnMatrix	C (const ColumnVector &qp)
	Joint torque due to centrifugal and Corriolis based on Recursive Newton-Euler formulation.
virtual void	delta_torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp, const ColumnVector &dq, const ColumnVector &dqp, const ColumnVector &dqpp, ColumnVector &torque, ColumnVector &dtorque)
	Delta torque dynamics.
virtual void	dq_torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp, const ColumnVector &dq, ColumnVector &torque, ColumnVector &dtorque)
	Delta torque due to delta joint position.
virtual void	dqp_torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &dqp, ColumnVector &torque, ColumnVector &dtorque)
	Delta torque due to delta joint velocity.
virtual void	dTdqi (Matrix &dRot, ColumnVector &dp, const int i)
	Partial derivative of the robot position (homogeneous transf.)
virtual ReturnMatrix	dTdqi (const int i)
	Partial derivative of the robot position (homogeneous transf.)
virtual ReturnMatrix	G ()
	Joint torque due to gravity based on Recursive Newton-Euler formulation.
ReturnMatrix	inv_kin (const Matrix &Tobj, const int mj=0)
	Overload inv_kin function.
virtual ReturnMatrix	inv_kin (const Matrix &Tobj, const int mj, const int endlink, bool &converge)
	Inverse kinematics solutions.
virtual ReturnMatrix	inv_kin_puma (const Matrix &Tobj, bool &converge)
	Analytic Puma inverse kinematics.
virtual ReturnMatrix	inv_kin_rhino (const Matrix &Tobj, bool &converge)
	Analytic Rhino inverse kinematics.
virtual ReturnMatrix	inv_kin_schilling (const Matrix &Tobj, bool &converge)
	Analytic Schilling inverse kinematics.
virtual ReturnMatrix	jacobian (const int ref=0) const
	Jacobian of mobile links expressed at frame ref.
virtual ReturnMatrix	jacobian (const int endlink, const int ref) const
	Jacobian of mobile joints up to endlink expressed at frame ref.
virtual ReturnMatrix	jacobian_dot (const int ref=0) const
	Jacobian derivative of mobile joints expressed at frame ref.
virtual void	kine_pd (Matrix &Rot, ColumnVector &pos, ColumnVector &pos_dot, const int ref) const
	Direct kinematics with velocity.
	mRobot (const int ndof=1)
	Constructor.
	mRobot (const Matrix &initrobot_motor)
	Constructor.
	mRobot (const Matrix &initrobot, const Matrix &initmotor)
	Constructor.
	mRobot (const mRobot &x)
	Copy constructor.
	mRobot (const std::string &filename, const std::string &robotName)
virtual void	robotType_inv_kin ()
	Identify inverse kinematics familly.
virtual ReturnMatrix	torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp)
	Joint torque, without contact force, based on Recursive Newton-Euler formulation.
virtual ReturnMatrix	torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp, const ColumnVector &Fext_, const ColumnVector &Next_)
	Joint torque based on Recursive Newton-Euler formulation.
virtual ReturnMatrix	torque_novelocity (const ColumnVector &qpp)
	Joint torque. when joint velocity is 0, based on Recursive Newton-Euler formulation.
virtual	~mRobot ()
	Destructor.

Detailed Description

Modified DH notation robot class.

Definition at line 389 of file robot.h.

Constructor & Destructor Documentation

mRobot::mRobot ( const int ndof = 1 )

Constructor.

Definition at line 1311 of file robot.cpp.

mRobot::mRobot ( const Matrix & initrobot_motor )

Constructor.

Definition at line 1320 of file robot.cpp.

mRobot::mRobot	(	const Matrix &	initrobot,
		const Matrix &	initmotor
	)

Constructor.

Definition at line 1329 of file robot.cpp.

mRobot::mRobot ( const mRobot & x )

Copy constructor.

Definition at line 1349 of file robot.cpp.

mRobot::mRobot	(	const std::string &	filename,
		const std::string &	robotName
	)

virtual mRobot::~mRobot ( ) [inline, virtual]

Destructor.

Definition at line 396 of file robot.h.

Member Function Documentation

ReturnMatrix mRobot::C ( const ColumnVector & qp ) [virtual]

Joint torque due to centrifugal and Corriolis based on Recursive Newton-Euler formulation.

Implements Robot_basic.

Definition at line 636 of file dynamics.cpp.

void mRobot::delta_torque	(	const ColumnVector &	q,
		const ColumnVector &	qp,
		const ColumnVector &	qpp,
		const ColumnVector &	dq,
		const ColumnVector &	dqp,
		const ColumnVector &	dqpp,
		ColumnVector &	ltorque,
		ColumnVector &	dtorque
	)		`[virtual]`

Delta torque dynamics.

This function computes

$\delta \tau = D(q) \delta \ddot{q} + S_1(q,\dot{q}) \delta \dot{q} + S_2(q,\dot{q},\ddot{q}) \delta q$

Murray and Neuman Cite_: Murray86 have developed an efficient recursive linearized Newton-Euler formulation. In order to apply the RNE as presented in let us define the following variables

$p_{di} = \frac{\partial p_i}{\partial d_i} = \left [ \begin{array}{ccc} 0 & \sin \alpha_i & \cos \alpha_i \end{array} \right ]^T$

$Q = \left [ \begin{array}{ccc} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{array} \right ]$

Forward Iterations for $i=1, 2, \ldots, n$ . Initialize: $\delta \omega_0 = \delta \dot{\omega}_0 = \delta \dot{v}_0 = 0$ .

$\delta \omega_i = R_i^T \delta \omega_{i-1} + \sigma_i (z_0 \delta \dot{\theta}_i - QR_i^T \omega_i \delta \theta_i)$

$\delta \dot{\omega}_i = R_i^T \delta \dot{w}_{i-1} + \sigma_i [R_i^T \delta \omega_{i-1} \times z_0 \dot{\theta}_i + R_i^T \omega_{i-1} \times z_0 \delta \dot{\theta}_i + z_0 \ddot{\theta}_i - (QR_i^T \dot{\omega}_{i-1} + QR_i^T \omega_{i-1} \times \omega{z}_0 \dot{\theta}_i) \delta \theta_i ]$

$\delta \dot{v}_i = R_i^T\Big(\delta \dot{\omega}_{i-1} \times p_i + \delta \omega_{i-1} \times(\omega_{i-1} \times p_i) + \omega_{i-1} \times( \delta \omega_{i-1} \times p_i) + \delta \dot{v}_i\Big) + (1-\sigma_i)\Big(2\delta \omega_i \times z_0\dot{d}_i + 2\omega_i \times z_0 \delta \dot{d}_i + z_0 \delta \ddot{d}_i\Big) - \sigma_i QR_i^T \Big(\dot{\omega}_{i-1} \times p_i + \omega_{i-1} \times(w_{i-1}\times p_i) + \dot{v}_i\Big) \delta \theta_i + (1-\sigma_i) R_i^T \Big(\dot{\omega}_{i-1} \times p_{di} + \omega_{i-1} \times(\omega_{i-1}\times p_{di})\Big) \delta d_i$

Backward Iterations for $i=n, n-1, \ldots, 1$ . Initialize: $\delta f_{n+1} = \delta n_{n+1} = 0$ .

$\delta \dot{v}_{ci} = \delta \dot{v}_i + \delta \dot{\omega}_i\times r_i + \delta \omega_i \times(\omega_i \times r_i) + \omega_i \times ( \delta \omega_i \times r_i)$

$\delta F_i = m_i \delta \dot{v}_{ci}$

$\delta N_i = I_{ci} \delta \dot{\omega}_i + \delta \omega_i \times (I_{ci}\omega_i) + \omega_i \times (I_{ci} \delta \omega_i)$

$\delta f_i = R_{i+1} \delta f_{i+1} + \delta F_i + \sigma_{i+1} R_{i+1} Qf_{i+1} \delta \theta_{i+1}$

$\delta n_i = \delta N_i + R_{i+1} \delta n_{i+1} + r_i\times \delta F_i + p_{i+1} \times R_{i+1} \delta f_{i+1} + \sigma_{i+1} \Big( R_{i+1} Qn_{i+1} + p_{i+1} \times R_{i+1} Qf_{i+1} \Big) \delta \theta_{i+1} + (1-\sigma_{i+1} ) p_{di+1} p_{di+1} \times R_{i+1} f_{i+1} \delta d_{i+1}$

$\delta \tau_i = \sigma \delta n_i^T z_0 + (1 - \sigma_i) \delta f_i^T z_0$

Implements Robot_basic.

Definition at line 291 of file delta_t.cpp.

void mRobot::dq_torque	(	const ColumnVector &	q,
		const ColumnVector &	qp,
		const ColumnVector &	qpp,
		const ColumnVector &	dq,
		ColumnVector &	ltorque,
		ColumnVector &	dtorque
	)		`[virtual]`

Delta torque due to delta joint position.

This function computes $S_2(q, \dot{q}, \ddot{q})\delta q$ . See mRobot::delta_torque for equations.

Implements Robot_basic.

Definition at line 205 of file comp_dq.cpp.

void mRobot::dqp_torque	(	const ColumnVector &	q,
		const ColumnVector &	qp,
		const ColumnVector &	dqp,
		ColumnVector &	ltorque,
		ColumnVector &	dtorque
	)		`[virtual]`

Delta torque due to delta joint velocity.

This function computes $S_1(q, \dot{q}, \ddot{q})\delta \dot{q}$ . See mRobot::delta_torque for equations.

Implements Robot_basic.

Definition at line 188 of file comp_dqp.cpp.

void mRobot::dTdqi	(	Matrix &	dRot,
		ColumnVector &	dp,
		const int	i
	)		`[virtual]`

Partial derivative of the robot position (homogeneous transf.)

This function computes the partial derivatives:

$\frac{\partial{}^0 T_n}{\partial q_i} = {}^0 T_{i} Q_i \; {}^{i} T_n$

with

$Q_i = \left [ \begin{array}{cccc} 0 & -1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right ]$

for a revolute joint and

$Q_i = \left [ \begin{array}{cccc} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \end{array} \right ]$

for a prismatic joint.

$dRot$ and $dp$ are modified on output.

Implements Robot_basic.

Definition at line 582 of file kinemat.cpp.

ReturnMatrix mRobot::dTdqi ( const int i ) [virtual]

Partial derivative of the robot position (homogeneous transf.)

See mRobot::dTdqi(Matrix & dRot, ColumnVector & dp, const int i) for equations.

Implements Robot_basic.

Definition at line 664 of file kinemat.cpp.

ReturnMatrix mRobot::G ( ) [virtual]

Joint torque due to gravity based on Recursive Newton-Euler formulation.

Implements Robot_basic.

Definition at line 599 of file dynamics.cpp.

ReturnMatrix mRobot::inv_kin	(	const Matrix &	Tobj,
		const int	mj = `0`
	)		`[virtual]`

Overload inv_kin function.

Reimplemented from Robot_basic.

Definition at line 617 of file invkine.cpp.

ReturnMatrix mRobot::inv_kin	(	const Matrix &	Tobj,
		const int	mj,
		const int	endlink,
		bool &	converge
	)		`[virtual]`

Inverse kinematics solutions.

The solution is based on the analytic inverse kinematics if robot type (familly) is Rhino or Puma, otherwise used the numerical algoritm defined in Robot_basic class.

Reimplemented from Robot_basic.

Definition at line 625 of file invkine.cpp.

ReturnMatrix mRobot::inv_kin_puma	(	const Matrix &	Tobj,
		bool &	converge
	)		`[virtual]`

Analytic Puma inverse kinematics.

converge will be false if the desired end effector pose is outside robot range.

Implements Robot_basic.

Definition at line 755 of file invkine.cpp.

ReturnMatrix mRobot::inv_kin_rhino	(	const Matrix &	Tobj,
		bool &	converge
	)		`[virtual]`

Analytic Rhino inverse kinematics.

converge will be false if the desired end effector pose is outside robot range.

Implements Robot_basic.

Definition at line 650 of file invkine.cpp.

ReturnMatrix mRobot::inv_kin_schilling	(	const Matrix &	Tobj,
		bool &	converge
	)		`[virtual]`

Analytic Schilling inverse kinematics.

converge will be false if the desired end effector pose is outside robot range.

Implements Robot_basic.

Definition at line 915 of file invkine.cpp.

virtual ReturnMatrix mRobot::jacobian ( const int ref = 0 ) const [inline, virtual]

Jacobian of mobile links expressed at frame ref.

Reimplemented from Robot_basic.

Definition at line 405 of file robot.h.

ReturnMatrix mRobot::jacobian	(	const int	endlink,
		const int	ref
	)		const `[virtual]`

Jacobian of mobile joints up to endlink expressed at frame ref.

See Robot::jacobian for equations.

Implements Robot_basic.

Definition at line 682 of file kinemat.cpp.

ReturnMatrix mRobot::jacobian_dot ( const int ref = 0 ) const [virtual]

Jacobian derivative of mobile joints expressed at frame ref.

See Robot::jacobian_dot for equations.

Implements Robot_basic.

Definition at line 736 of file kinemat.cpp.

void mRobot::kine_pd	(	Matrix &	Rot,
		ColumnVector &	pos,
		ColumnVector &	pos_dot,
		const int	j
	)		const `[virtual]`

Direct kinematics with velocity.

Parameters:

Rot,:	Frame j rotation matrix w.r.t to the base frame.
pos,:	Frame j position vector wr.r.t to the base frame.
pos_dot,:	Frame j velocity vector w.r.t to the base frame.
j,:	Frame j. Print an error on the console if j is out of range.

Implements Robot_basic.

Definition at line 552 of file kinemat.cpp.

void mRobot::robotType_inv_kin ( ) [virtual]

Identify inverse kinematics familly.

Identify the inverse kinematics analytic solution based on the similarity of the robot DH parameters and the DH parameters of know robots (ex: Puma, Rhino, ...). The inverse kinematics will be based on a numerical alogorithm if there is no match .

Implements Robot_basic.

Definition at line 1354 of file robot.cpp.

ReturnMatrix mRobot::torque	(	const ColumnVector &	q,
		const ColumnVector &	qp,
		const ColumnVector &	qpp
	)		`[virtual]`

Joint torque, without contact force, based on Recursive Newton-Euler formulation.

Implements Robot_basic.

Definition at line 412 of file dynamics.cpp.

ReturnMatrix mRobot::torque	(	const ColumnVector &	q,
		const ColumnVector &	qp,
		const ColumnVector &	qpp,
		const ColumnVector &	Fext_,
		const ColumnVector &	Next_
	)		`[virtual]`

Joint torque based on Recursive Newton-Euler formulation.

In order to apply the RNE, let us define the following variables (referenced in the $i^{th}$ coordinate frame if applicable):

$\sigma_i$ is the joint type; $\sigma_i = 1$ for a revolute joint and $\sigma_i = 0$ for a prismatic joint.

$z_0 = \left [ \begin{array}{ccc} 0 & 0 & 1 \end{array} \right ]^T$

$p_i = \left [ \begin{array}{ccc} a_{i-1} & -d_i sin \alpha_{i-1} & d_i cos \alpha_{i-1} \end{array} \right ]^T$ is the position of the $i^{th}$ with respect to the $i-1^{th}$ frame.

Forward Iterations for $i=1, 2, \ldots, n$ . Initialize: $\omega_0 = \dot{\omega}_0 = 0$ and $\dot{v}_0 = - g$ .

$\omega_i = R_i^T\omega_{i-1} + \sigma_i z_0\dot{\theta_i}$

$\dot{\omega}_i = R_i^T\dot{\omega}_{i-1} + \sigma_i R_i^T\omega_{i-1}\times z_0 \dot{\theta}_i + \sigma_iz_0\ddot{\theta}_i$

$\dot{v}_i = R_i^T(\dot{\omega}_{i-1}\times p_i + \omega_{i-1}\times(\omega_{i-1}\times p_i) + \dot{v}_{i-1}) + (1 - \sigma_i)(2\omega_i\times z_0 dot{d}_i + z_0\ddot{d}_i)$

Backward Iterations for $i=n, n-1, \ldots, 1$ . Initialize: $f_{n+1} = n_{n+1} = 0$ .

$\dot{v}_{ci} = \dot{\omega}_i\times r_i + \omega_i\times(\omega_i\times r_i) + v_i$

$F_i = m_i \dot{v}_{ci}$

$N_i = I_{ci}\ddot{\omega}_i\ + \omega_i \times I_{ci}\omega_i$

$f_i = R_{i+1}f_{i+1} + F_i$

$n_i = N_i + R_{i+1} n_{i+1} + r_i \times F_i + p_{i+1}\times R_{i+1}f_{i+1}$

$\tau_i = \sigma_i n_i^T z_0 + (1 - \sigma_i) f_i^T z_0$

Implements Robot_basic.

Definition at line 422 of file dynamics.cpp.

ReturnMatrix mRobot::torque_novelocity ( const ColumnVector & qpp ) [virtual]

Joint torque. when joint velocity is 0, based on Recursive Newton-Euler formulation.

Implements Robot_basic.

Definition at line 555 of file dynamics.cpp.

The documentation for this class was generated from the following files:

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation