Functions
const arma::mat	mr::MassMatrix (const arma::vec &thetalist, const std::vector< arma::mat44 > &Mlist, const std::vector< arma::mat66 > &Glist, const std::vector< arma::vec6 > &Slist)
	Computes the mass matrix of an open chain robot based on the given configuration. More...

const arma::vec	mr::VelQuandraticForces (const arma::vec &thetalist, const arma::vec &dthetalist, const std::vector< arma::mat44 > Mlist, const std::vector< arma::mat66 > &Glist, const std::vector< arma::vec6 > &Slist)
	Computes the Coriolis and centripetal terms in the inverse dynamics of an open chain robot. More...

const arma::vec	mr::GravityForces (const arma::vec &thetalist, const arma::vec3 &g, const std::vector< arma::mat44 > &Mlist, const std::vector< arma::mat66 > &Glist, const std::vector< arma::vec6 > &Slist)
	Computes the joint forces/torques an open chain robot requires to overcome gravity at its configuration. More...

const arma::vec	mr::EndEffectorForces (const arma::vec &thetalist, const arma::vec6 &Ftip, const std::vector< arma::mat44 > &Mlist, const std::vector< arma::mat66 > &Glist, const std::vector< arma::vec6 > &Slist)
	Computes the joint forces/torques an open chain robot requires only to create the end-effector force Ftip. More...

const arma::vec	mr::ForwardDynamics (const arma::vec &thetalist, const arma::vec &dthetalist, const arma::vec &taulist, const arma::vec3 &g, const arma::vec6 &Ftip, const std::vector< arma::mat44 > &Mlist, const std::vector< arma::mat66 > &Glist, const std::vector< arma::vec6 > &Slist)
	Computes forward dynamics in the space frame for an open chain robot. More...

const std::tuple< const arma::vec, const arma::vec >	mr::EulerStep (const arma::vec &thetalist, const arma::vec &dthetalist, const arma::vec &ddthetalist, const double dt)
	Compute the joint angles and velocities at the next timestep using first order Euler integration. More...

const std::tuple< const arma::vec, const arma::vec >	mr::RK4Step (const arma::vec &thetalist, const arma::vec &dthetalist, const std::function< const std::tuple< const arma::vec, const arma::vec >(const arma::vec &, const arma::vec &) > &f, const double dt)
	Compute the joint angles and velocities at the next timestep using Runge–Kutta methods integration. More...

const std::vector< arma::vec >	mr::InverseDynamicsTrajectory (const std::vector< arma::vec > &thetamat, const std::vector< arma::vec > &dthetamat, const std::vector< arma::vec > &ddthetamat, const arma::vec3 &g, const std::vector< arma::vec6 > &Ftipmat, const std::vector< arma::mat44 > &Mlist, const std::vector< arma::mat66 > &Glist, const std::vector< arma::vec6 > &Slist)
	Calculates the joint forces/torques required to move the serial chain along the given trajectory using inverse dynamics. More...

const std::tuple< const std::vector< arma::vec >, const std::vector< arma::vec > >	mr::ForwardDynamicsTrajectory (const arma::vec &thetalist, const arma::vec &dthetalist, const std::vector< arma::vec > &taumat, const arma::vec3 &g, const std::vector< arma::vec6 > &Ftipmat, const std::vector< arma::mat44 > &Mlist, const std::vector< arma::mat66 > &Glist, const std::vector< arma::vec6 > &Slist, const double dt, const int intRes)
	Simulates the motion of a serial chain given an open-loop history of joint forces/torques. More...

Detailed Description

Function Documentation

◆ EndEffectorForces()

const arma::vec mr::EndEffectorForces	(	const arma::vec &	thetalist,
		const arma::vec6 &	Ftip,
		const std::vector< arma::mat44 > &	Mlist,
		const std::vector< arma::mat66 > &	Glist,
		const std::vector< arma::vec6 > &	Slist
	)

Computes the joint forces/torques an open chain robot requires only to create the end-effector force Ftip.

Parameters

thetalist	A list of joint variables
Ftip	Spatial force applied by the end-effector expressed in frame {n+1}
Mlist	List of link frames i relative to i-1 at the home position
Glist	Spatial inertia matrices Gi of the links
Slist	Screw axes Si of the joints in a space frame, in the format of a matrix with axes as the columns

Returns: The joint forces and torques required only to create the end-effector force Ftip

◆ EulerStep()

const std::tuple< const arma::vec, const arma::vec > mr::EulerStep	(	const arma::vec &	thetalist,
		const arma::vec &	dthetalist,
		const arma::vec &	ddthetalist,
		const double	dt
	)

Compute the joint angles and velocities at the next timestep using first order Euler integration.

Parameters

thetalist	n-vector of joint variables
dthetalist	n-vector of joint rates
ddthetalist	n-vector of joint accelerations
dt	The timestep delta t

Returns: thetalistNext: Vector of joint variables after dt from first order Euler integration; dthetalistNext: Vector of joint rates after dt from first order Euler integration

◆ ForwardDynamics()

const arma::vec mr::ForwardDynamics	(	const arma::vec &	thetalist,
		const arma::vec &	dthetalist,
		const arma::vec &	taulist,
		const arma::vec3 &	g,
		const arma::vec6 &	Ftip,
		const std::vector< arma::mat44 > &	Mlist,
		const std::vector< arma::mat66 > &	Glist,
		const std::vector< arma::vec6 > &	Slist
	)

Computes forward dynamics in the space frame for an open chain robot.

Parameters

thetalist	A list of joint variables
dthetalist	A list of joint rates
taulist	An n-vector of joint forces/torques
g	Gravity vector g
Ftip	Spatial force applied by the end-effector expressed in frame {n+1}
Mlist	List of link frames i relative to i-1 at the home position
Glist	Spatial inertia matrices Gi of the links
Slist	Screw axes Si of the joints in a space frame, in the format of a matrix with axes as the columns

Returns: The resulting joint accelerations

This function computes ddthetalist by solving: Mlist(thetalist) * ddthetalist = taulist - c(thetalist,dthetalist) - g(thetalist) - Jtr(thetalist) * Ftip

◆ ForwardDynamicsTrajectory()

const std::tuple< const std::vector< arma::vec >, const std::vector< arma::vec > > mr::ForwardDynamicsTrajectory	(	const arma::vec &	thetalist,
		const arma::vec &	dthetalist,
		const std::vector< arma::vec > &	taumat,
		const arma::vec3 &	g,
		const std::vector< arma::vec6 > &	Ftipmat,
		const std::vector< arma::mat44 > &	Mlist,
		const std::vector< arma::mat66 > &	Glist,
		const std::vector< arma::vec6 > &	Slist,
		const double	dt,
		const int	intRes
	)

Simulates the motion of a serial chain given an open-loop history of joint forces/torques.

Parameters

thetalist	n-vector of initial joint variables
dthetalist	n-vector of initial joint rates
taumat	An N x n matrix of joint forces/torques, where each row is the joint effort at any time step
g	Gravity vector g
Ftipmat	An N x 6 matrix of spatial forces applied by the end- effector (If there are no tip forces the user should input a zero and a zero matrix will be used)
Mlist	List of link frames {i} relative to {i-1} at the home position
Glist	Spatial inertia matrices Gi of the links
Slist	Screw axes Si of the joints in a space frame, in the format of a matrix with axes as the columns
dt	The timestep between consecutive joint forces/torques
intRes	Integration resolution is the number of times integration (Euler) takes places between each time step. Must be an integer value greater than or equal to 1

Returns: thetamat: The N x n matrix of robot joint angles resulting from the specified joint forces/torques; dthetamat: The N x n matrix of robot joint velocities

This function calls a numerical integration procedure that uses ForwardDynamics.

◆ GravityForces()

const arma::vec mr::GravityForces	(	const arma::vec &	thetalist,
		const arma::vec3 &	g,
		const std::vector< arma::mat44 > &	Mlist,
		const std::vector< arma::mat66 > &	Glist,
		const std::vector< arma::vec6 > &	Slist
	)

Computes the joint forces/torques an open chain robot requires to overcome gravity at its configuration.

Parameters

thetalist	A list of joint variables
g	3-vector for gravitational acceleration
Mlist	List of link frames i relative to i-1 at the home position
Glist	Spatial inertia matrices Gi of the links
Slist	Screw axes Si of the joints in a space frame, in the format of a matrix with axes as the columns

Returns: The joint forces/torques required to overcome gravity at thetalist

This function calls InverseDynamics with Ftip = 0, dthetalist = 0, and ddthetalist = 0.

◆ InverseDynamicsTrajectory()

const std::vector< arma::vec > mr::InverseDynamicsTrajectory	(	const std::vector< arma::vec > &	thetamat,
		const std::vector< arma::vec > &	dthetamat,
		const std::vector< arma::vec > &	ddthetamat,
		const arma::vec3 &	g,
		const std::vector< arma::vec6 > &	Ftipmat,
		const std::vector< arma::mat44 > &	Mlist,
		const std::vector< arma::mat66 > &	Glist,
		const std::vector< arma::vec6 > &	Slist
	)

Calculates the joint forces/torques required to move the serial chain along the given trajectory using inverse dynamics.

Parameters

thetamat	An N x n matrix of robot joint variables
dthetamat	An N x n matrix of robot joint velocities
ddthetamat	An N x n matrix of robot joint accelerations
g	Gravity vector g
Ftipmat	An N x 6 matrix of spatial forces applied by the end- effector (If there are no tip forces the user should input a zero and a zero matrix will be used)
Mlist	List of link frames i relative to i-1 at the home position
Glist	Spatial inertia matrices Gi of the links
Slist	Screw axes Si of the joints in a space frame, in the format of a matrix with axes as the columns

Returns: The N x n matrix of joint forces/torques for the specified trajectory, where each of the N rows is the vector of joint forces/torques at each time step

◆ MassMatrix()

const arma::mat mr::MassMatrix	(	const arma::vec &	thetalist,
		const std::vector< arma::mat44 > &	Mlist,
		const std::vector< arma::mat66 > &	Glist,
		const std::vector< arma::vec6 > &	Slist
	)

Computes the mass matrix of an open chain robot based on the given configuration.

Parameters

thetalist	A list of joint variables
Mlist	List of link frames i relative to i-1 at the home position
Glist	Spatial inertia matrices Gi of the links
Slist	Screw axes Si of the joints in a space frame, in the format of a matrix with axes as the columns

Returns: The numerical inertia matrix M(thetalist) of an n-joint serial chain at the given configuration thetalist

This function calls InverseDynamics n times, each time passing a ddthetalist vector with a single element equal to one and all other inputs set to zero. Each call of InverseDynamics generates a single column, and these columns are assembled to create the inertia matrix.

◆ RK4Step()

const std::tuple< const arma::vec, const arma::vec > mr::RK4Step	(	const arma::vec &	thetalist,
		const arma::vec &	dthetalist,
		const std::function< const std::tuple< const arma::vec, const arma::vec >(const arma::vec &, const arma::vec &) > &	f,
		const double	dt
	)

Compute the joint angles and velocities at the next timestep using Runge–Kutta methods integration.

Parameters

thetalist	n-vector of joint variables
dthetalist	n-vector of joint rates
f	function that calculate the ddthetalist
dt	The timestep delta t

Returns: thetalistNext: Vector of joint variables after dt from Runge–Kutta methods integration; dthetalistNext: Vector of joint rates after dt from Runge–Kutta methods integration

◆ VelQuandraticForces()

const arma::vec mr::VelQuandraticForces	(	const arma::vec &	thetalist,
		const arma::vec &	dthetalist,
		const std::vector< arma::mat44 >	Mlist,
		const std::vector< arma::mat66 > &	Glist,
		const std::vector< arma::vec6 > &	Slist
	)

Computes the Coriolis and centripetal terms in the inverse dynamics of an open chain robot.

Parameters

thetalist	A list of joint variables
dthetalist	A list of joint rates
Mlist	List of link frames i relative to i-1 at the home position
Glist	Spatial inertia matrices Gi of the links
Slist	Screw axes Si of the joints in a space frame, in the format of a matrix with axes as the columns.

Returns: The vector c(thetalist,dthetalist) of Coriolis and centripetal terms for a given thetalist and dthetalist.

This function calls InverseDynamics with g = 0, Ftip = 0, and ddthetalist = 0.

Functions

Detailed Description

Function Documentation

◆ EndEffectorForces()

◆ EulerStep()

◆ ForwardDynamics()

◆ ForwardDynamicsTrajectory()

◆ GravityForces()

◆ InverseDynamicsTrajectory()

◆ MassMatrix()

◆ RK4Step()

◆ VelQuandraticForces()