ROBOOP::Robot

ROBOOP::Robot Class Reference

#include <robot.h>

Inheritance diagram for ROBOOP::Robot:

Detailed Description

DH notation robot class.

Definition at line 385 of file robot.h.

Public Member Functions

Robot (const int ndof=1)

Constructor.

Robot (const Matrix &initrobot)

Constructor.

Robot (const Matrix &initrobot, const Matrix &initmotor)

Constructor.

Robot (const Robot &x)

Copy constructor.

Robot (const string &filename, const string &robotName)

Constructor.

Robot (const Config &robData, const string &robotName)

~Robot ()

Destructor.

Robot & operator= (const Robot &x)

Overload = operator.

virtual void robotType_inv_kin ()

Identify inverse kinematics familly.

virtual void kine_pd (Matrix &Rot, ColumnVector &pos, ColumnVector &pos_dot, const int ref) const

Direct kinematics with velocity.

virtual ReturnMatrix inv_kin (const Matrix &Tobj, const int mj=0)

Overload inv_kin function.

virtual ReturnMatrix inv_kin (const Matrix &Tobj, const int mj, bool &converge)

Numerical inverse kinematics. See inv_kin(const Matrix & Tobj, const int mj, const int endlink, bool & converge).

virtual ReturnMatrix inv_kin (const Matrix &Tobj, const int mj, const int endlink, bool &converge)

Inverse kinematics solutions.

virtual ReturnMatrix inv_kin_pos (const ColumnVector &Pobj, const int mj, const int endlink, const ColumnVector &Plink, bool &converge)

Inverse kinematics solutions.

virtual ReturnMatrix inv_kin_orientation (const Matrix &Robj, const int mj, const int endlink, bool &converge)

Inverse kinematics solutions.

virtual ReturnMatrix inv_kin_rhino (const Matrix &Tobj, bool &converge)

Analytic Rhino inverse kinematics.

virtual ReturnMatrix inv_kin_puma (const Matrix &Tobj, bool &converge)

Analytic Puma inverse kinematics.

virtual ReturnMatrix inv_kin_ers_pos (const ColumnVector &Pobj, const int endlink, const ColumnVector &Plink, bool &converge)

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 links 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 dTdqi (Matrix &dRot, ColumnVector &dpos, const int i)

Partial derivative of the robot position (homogeneous transf.) See dTdqi(Matrix & dRot, ColumnVector & dpos, const int i, const int endlink).

virtual ReturnMatrix dTdqi (const int i)

Partial derivative of the robot position (homogeneous transf.) See dTdqi(Matrix & dRot, ColumnVector & dpos, const int i, const int endlink).

virtual void dTdqi (Matrix &dRot, ColumnVector &dpos, const int i, const int endlink)

Partial derivative of the robot position (homogeneous transf.).

virtual ReturnMatrix dTdqi (const int i, const int endlink)

Partial derivative of the robot position (homogeneous transf.).

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 void delta_torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp, const ColumnVector &dq, const ColumnVector &dqp, const ColumnVector &dqpp, ColumnVector &ltorque, 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 ReturnMatrix G ()

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

virtual ReturnMatrix C (const ColumnVector &qp)

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

Protected Member Functions

Real computeFirstERSLink (int curlink, const ColumnVector &Pobj, const int endlink, const ColumnVector &Plink, Real min, Real max, bool &converge)

Real computeSecondERSLink (int curlink, const ColumnVector &Pobj, const int endlink, const ColumnVector &Plink, bool invert, Real min, Real max, bool &converge)

Real computeThirdERSLink (int curlink, const ColumnVector &Pobj, const int endlink, const ColumnVector &Plink, bool invert, Real min, Real max, bool &converge)

Constructor & Destructor Documentation

ROBOOP::Robot::Robot ( const int ndof = 1 ) [explicit]

Constructor.

Definition at line 1346 of file robot.cpp.

ROBOOP::Robot::Robot ( const Matrix & initrobot ) [explicit]

Constructor.

Definition at line 1355 of file robot.cpp.

ROBOOP::Robot::Robot	(	const Matrix &	initrobot,
		const Matrix &	initmotor
	)			`[explicit]`

Constructor.

Definition at line 1364 of file robot.cpp.

ROBOOP::Robot::Robot ( const Robot & x )

Copy constructor.

Definition at line 1394 of file robot.cpp.

ROBOOP::Robot::Robot	(	const string &	filename,
		const string &	robotName
	)			`[explicit]`

Constructor.

Definition at line 1374 of file robot.cpp.

ROBOOP::Robot::Robot	(	const Config &	robData,
		const string &	robotName
	)			`[explicit]`

Definition at line 1384 of file robot.cpp.

ROBOOP::Robot::~Robot ( ) [inline]

Destructor.

Definition at line 394 of file robot.h.

Member Function Documentation

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

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

Implements ROBOOP::Robot_basic.

Definition at line 355 of file dynamics.cpp.

Real ROBOOP::Robot::computeFirstERSLink	(	int	curlink,
		const ColumnVector &	Pobj,
		const int	endlink,
		const ColumnVector &	Plink,
		Real	min,
		Real	max,
		bool &	converge
	)			`[protected]`

Definition at line 947 of file invkine.cpp.

Referenced by computeSecondERSLink(), and inv_kin_ers_pos().

Real ROBOOP::Robot::computeSecondERSLink	(	int	curlink,
		const ColumnVector &	Pobj,
		const int	endlink,
		const ColumnVector &	Plink,
		bool	invert,
		Real	min,
		Real	max,
		bool &	converge
	)			`[protected]`

Definition at line 964 of file invkine.cpp.

Referenced by inv_kin_ers_pos().

Real ROBOOP::Robot::computeThirdERSLink	(	int	curlink,
		const ColumnVector &	Pobj,
		const int	endlink,
		const ColumnVector &	Plink,
		bool	invert,
		Real	min,
		Real	max,
		bool &	converge
	)			`[protected]`

Definition at line 1006 of file invkine.cpp.

Referenced by inv_kin_ers_pos().

void ROBOOP::Robot::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: $\delta \omega_0 = \delta \dot{\omega}_0 = \delta \dot{v}_0 = 0$ .

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

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

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

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

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

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

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

$\delta f_i = R_{i+1} [ \delta f_{i+1} ] + \delta F_{i} + \sigma_{i+1} Q R_{i+1} [ f_{i+1} ] \delta \theta_{i+1}$

$\delta n_i = R_{i+1} [ \delta n_{i+1} ] + \delta N_{i} + p_{i} \times \delta f_{i} + r_{i} \times \delta F_{i} + (1 - \sigma_i) (p_{di} \times f_{i}) \delta d_i + \sigma_{i+1} Q R_{i+1} [ n_{i+1} ] \delta \theta_{i+1}$

$\delta \tau_i = \sigma_i [ \delta n_i^T (R_i^T z_0) - n_i^T (R_i^T Q z_0) \delta \theta_i] + (1 -\sigma_i) [ \delta f_i^T (R_i^T z_0) ]$

Implements ROBOOP::Robot_basic.

Definition at line 63 of file delta_t.cpp.

void ROBOOP::Robot::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 Robot::delta_torque for equations.

Implements ROBOOP::Robot_basic.

Definition at line 65 of file comp_dq.cpp.

void ROBOOP::Robot::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 Robot::delta_torque for equations.

Implements ROBOOP::Robot_basic.

Definition at line 63 of file comp_dqp.cpp.

ReturnMatrix ROBOOP::Robot::dTdqi	(	const int	i,
		const int	endlink
	)			`[virtual]`

Partial derivative of the robot position (homogeneous transf.).

See Robot::dTdqi(Matrix & dRot, ColumnVector & dpos, const int i, const int endlink) for equations.

Implements ROBOOP::Robot_basic.

Definition at line 539 of file kinemat.cpp.

void ROBOOP::Robot::dTdqi	(	Matrix &	dRot,
		ColumnVector &	dpos,
		const int	i,
		const int	endlink
	)			`[virtual]`

Partial derivative of the robot position (homogeneous transf.).

This function computes the partial derivatives:

$\frac{\partial{}^0 T_n}{\partial q_i} = {}^0 T_{i-1} Q_i \; {}^{i-1} T_n$

in standard notation and

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

in modified notation,

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 ROBOOP::Robot_basic.

Definition at line 454 of file kinemat.cpp.

virtual ReturnMatrix ROBOOP::Robot::dTdqi ( const int i ) [inline, virtual]

Partial derivative of the robot position (homogeneous transf.) See dTdqi(Matrix & dRot, ColumnVector & dpos, const int i, const int endlink).

Reimplemented from ROBOOP::Robot_basic.

Definition at line 413 of file robot.h.

virtual void ROBOOP::Robot::dTdqi	(	Matrix &	dRot,
		ColumnVector &	dpos,
		const int	i
	)			`[inline, virtual]`

Partial derivative of the robot position (homogeneous transf.) See dTdqi(Matrix & dRot, ColumnVector & dpos, const int i, const int endlink).

Reimplemented from ROBOOP::Robot_basic.

Definition at line 412 of file robot.h.

Referenced by dTdqi().

ReturnMatrix ROBOOP::Robot::G ( ) [virtual]

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

Implements ROBOOP::Robot_basic.

Definition at line 316 of file dynamics.cpp.

ReturnMatrix ROBOOP::Robot::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 ROBOOP::Robot_basic.

Definition at line 583 of file invkine.cpp.

virtual ReturnMatrix ROBOOP::Robot::inv_kin	(	const Matrix &	Tobj,
		const int	mj,
		bool &	converge
	)			`[inline, virtual]`

Numerical inverse kinematics. See inv_kin(const Matrix & Tobj, const int mj, const int endlink, bool & converge).

Reimplemented from ROBOOP::Robot_basic.

Definition at line 400 of file robot.h.

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

Overload inv_kin function.

Reimplemented from ROBOOP::Robot_basic.

Definition at line 575 of file invkine.cpp.

Referenced by inv_kin().

ReturnMatrix ROBOOP::Robot::inv_kin_ers_pos	(	const ColumnVector &	Pobj,
		const int	endlink,
		const ColumnVector &	Plink,
		bool &	converge
	)			`[virtual]`

Definition at line 912 of file invkine.cpp.

Referenced by inv_kin_pos().

ReturnMatrix ROBOOP::Robot::inv_kin_orientation	(	const Matrix &	Robj,
		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 ROBOOP::Robot_basic.

Definition at line 628 of file invkine.cpp.

ReturnMatrix ROBOOP::Robot::inv_kin_pos	(	const ColumnVector &	Pobj,
		const int	mj,
		const int	endlink,
		const ColumnVector &	Plink,
		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 ROBOOP::Robot_basic.

Definition at line 606 of file invkine.cpp.

ReturnMatrix ROBOOP::Robot::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 ROBOOP::Robot_basic.

Definition at line 750 of file invkine.cpp.

Referenced by inv_kin().

ReturnMatrix ROBOOP::Robot::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 ROBOOP::Robot_basic.

Definition at line 651 of file invkine.cpp.

Referenced by inv_kin().

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

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

The Jacobian expressed in based frame is

$^{0}J(q) = \left[ \begin{array}{cccc} ^{0}J_1(q) & ^{0}J_2(q) & \cdots & ^{0}J_n(q) \\ \end{array} \right]$

where $^{0}J_i(q)$ is defined by

$^{0}J_i(q) = \begin{array}{cc} \left[ \begin{array}{c} z_i \times ^{i}p_n \\ z_i \\ \end{array} \right] & \textrm{rotoid joint} \end{array}$

$^{0}J_i(q) = \begin{array}{cc} \left[ \begin{array}{c} z_i \\ 0 \\ \end{array} \right] & \textrm{prismatic joint} \\ \end{array}$

Expressed in a different frame the Jacobian is obtained by

$^{i}J(q) = \left[ \begin{array}{cc} ^{0}_iR^T & 0 \\ 0 & ^{0}_iR^T \end{array} \right] {^{0}}J(q)$

Implements ROBOOP::Robot_basic.

Definition at line 557 of file kinemat.cpp.

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

Jacobian of mobile links expressed at frame ref.

Reimplemented from ROBOOP::Robot_basic.

Definition at line 409 of file robot.h.

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

Jacobian derivative of mobile joints expressed at frame ref.

The Jacobian derivative expressed in based frame is

$^{0}\dot{J}(q,\dot{q}) = \left[ \begin{array}{cccc} ^{0}\dot{J}_1(q,\dot{q}) & ^{0}\dot{J}_2(q,\dot{q}) & \cdots & ^{0}\dot{J}_n(q,\dot{q}) \\ \end{array} \right]$

where $^{0}\dot{J}_i(q,\dot{q})$ is defined by

$^{0}\dot{J}_i(q,\dot{q}) = \begin{array}{cc} \left[ \begin{array}{c} \omega_{i-1} \times z_i \\ \omega_{i-1} \times ^{i-1}p_n + z_i \times ^{i-1}\dot{p}_n \end{array} \right] & \textrm{rotoid joint} \end{array}$

$^{0}\dot{J}_i(q,\dot{q}) = \begin{array}{cc} \left[ \begin{array}{c} 0 \\ 0 \\ \end{array} \right] & \textrm{prismatic joint} \\ \end{array}$

Expressed in a different frame the Jacobian derivative is obtained by

$^{i}J(q) = \left[ \begin{array}{cc} ^{0}_iR^T & 0 \\ 0 & ^{0}_iR^T \end{array} \right] {^{0}}J(q)$

Implements ROBOOP::Robot_basic.

Definition at line 653 of file kinemat.cpp.

void ROBOOP::Robot::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 ROBOOP::Robot_basic.

Definition at line 424 of file kinemat.cpp.

Robot & ROBOOP::Robot::operator= ( const Robot & x )

Overload = operator.

Definition at line 1398 of file robot.cpp.

void ROBOOP::Robot::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 ROBOOP::Robot_basic.

Definition at line 1405 of file robot.cpp.

Referenced by Robot().

ReturnMatrix ROBOOP::Robot::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 as presented in Murray 86, 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.

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

$p_i = \left [ \begin{array}{ccc} a_i & d_i \sin \alpha_i & d_i \cos \alpha_i \end{array} \right ]^T$ 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 $\dot{v}_0 = - g$ .

$\omega_i = R_i^T [\omega_{i-1} + \sigma_i z_0 \dot{\theta}_i ]$

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

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

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

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

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

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

$f_i = R_{i+1} [ f_{i+1} ] + F_{i}$

$n_i = R_{i+1} [ n_{i+1} ] + p_{i} \times f_{i} + N_{i} + r_{i} \times F_{i}$

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

Implements ROBOOP::Robot_basic.

Definition at line 143 of file dynamics.cpp.

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

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

Implements ROBOOP::Robot_basic.

Definition at line 130 of file dynamics.cpp.

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

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

Implements ROBOOP::Robot_basic.

Definition at line 267 of file dynamics.cpp.

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