Enumerations
enum class	Method : uint8_t { Cubic , Quintic }
	Trajectory generation method. More...

Functions
const arma::mat66	ad (const arma::vec6 &V)
	Calculate the 6x6 matrix [adV] of the given 6-vector. More...

const arma::vec	InverseDynamics (const arma::vec &thetalist, const arma::vec &dthetalist, const arma::vec &ddthetalist, const arma::vec &g, const arma::vec6 &Ftip, const std::vector< arma::mat44 > &Mlist, const std::vector< arma::mat66 > &Glist, const std::vector< arma::vec6 > &Slist)

const arma::mat	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	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	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	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	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 >	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 >	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 >	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 > >	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...

const arma::mat44	FKinBody (const arma::mat44 &M, const std::vector< arma::vec6 > &Blist, const arma::vec &thetalist)
	Computes forward kinematics in the body frame for an open chain robot. More...

const arma::mat44	FKinSpace (const arma::mat44 &M, const std::vector< arma::vec6 > &Slist, const arma::vec &thetalist)
	Computes forward kinematics in the space frame for an open chain robot. More...

const std::pair< const arma::vec, bool >	IKinBody (const std::vector< arma::vec6 > &Blist, const arma::mat44 &M, const arma::mat44 &T, const arma::vec &thetalist0, const double emog, const double ev)
	Computes inverse kinematics in the body frame for an open chain robot. More...

const std::pair< const arma::vec, bool >	IKinSpace (const std::vector< arma::vec6 > &Slist, const arma::mat44 &M, const arma::mat44 &T, const arma::vec &thetalist0, const double emog, const double ev)
	Computes inverse kinematics in the space frame for an open chain robot. More...

const arma::mat33	RotInv (const arma::mat33 &R)
	Inverts a rotation matrix. More...

const arma::mat33	VecToso3 (const arma::vec3 &omg)
	Converts a 3-vector to an so(3) representation. More...

const arma::vec3	so3ToVec (const arma::mat33 &so3mat)
	Converts an so(3) representation to a 3-vector. More...

const std::tuple< const arma::vec3, double >	AxisAng3 (const arma::vec3 &expc3)
	Converts a 3-vector of exponential coordinates for rotation into axis-angle form. More...

const arma::mat33	MatrixExp3 (const arma::mat33 &so3mat)
	Computes the matrix exponential of a matrix in so(3) More...

const arma::mat33	MatrixLog3 (const arma::mat33 &R)
	Computes the matrix logarithm of a rotation matrix. More...

const arma::mat44	RpToTrans (const arma::mat33 &R, const arma::vec3 &p)
	Converts a rotation matrix and a position vector into homogeneous transformation matrix. More...

const std::tuple< const arma::mat33, const arma::vec3 >	TransToRp (const arma::mat44 &T)
	Converts a homogeneous transformation matrix into a rotation matrix and position vector. More...

const arma::mat44	TransInv (const arma::mat44 &T)
	Inverts a homogeneous transformation matrix. More...

const arma::mat44	VecTose3 (const arma::vec6 &V)
	Converts a spatial velocity vector into a 4x4 matrix in se3. More...

const arma::vec6	se3ToVec (const arma::mat44 &se3mat)
	Converts an se3 matrix into a spatial velocity vector. More...

const arma::mat66	Adjoint (const arma::mat44 &T)
	Computes the adjoint representation of a homogeneous transformation matrix. More...

const arma::vec6	ScrewToAxis (const arma::vec3 &q, const arma::vec3 &s, const double h)
	Takes a parametric description of a screw axis and converts it to a normalized screw axis. More...

const std::tuple< const arma::vec6, double >	AxisAng6 (const arma::vec6 &expc6)
	Converts a 6-vector of exponential coordinates into screw axis-angle form. More...

const arma::mat44	MatrixExp6 (const arma::mat44 &se3mat)
	Computes the matrix exponential of an se3 representation of exponential coordinates. More...

const arma::mat44	MatrixLog6 (const arma::mat44 &T)
	Computes the matrix logarithm of a homogeneous transformation matrix. More...

const arma::mat33	ProjectToSO3 (const arma::mat33 &mat)
	Returns a projection of mat into SO(3) More...

const arma::mat44	ProjectToSE3 (const arma::mat44 &mat)
	Returns a projection of mat into SE(3) More...

double	DistanceToSO3 (const arma::mat33 &mat)
	Returns the Frobenius norm to describe the distance of mat from the SO(3) manifold. More...

double	DistanceToSE3 (const arma::mat44 &mat)
	Returns the Frobenius norm to describe the distance of mat from the SE(3) manifold. More...

bool	TestIfSO3 (const arma::mat33 &mat)
	Returns true if mat is close to or on the manifold SO(3) More...

bool	TestIfSE3 (const arma::mat44 &mat)
	Returns true if mat is close to or on the manifold SE(3) More...

const arma::vec	ComputeTorque (const arma::vec &thetalist, const arma::vec &dthetalist, const arma::vec &eint, const arma::vec3 &g, const std::vector< arma::mat44 > &Mlist, const std::vector< arma::mat66 > &Glist, const std::vector< arma::vec6 > &Slist, const arma::vec &thetalistd, const arma::vec &dthetalistd, const arma::vec &ddthetalistd, const double kp, const double ki, const double kd)
	Computes the joint control torques at a particular time instant. More...

const std::tuple< std::vector< arma::vec >, std::vector< arma::vec > >	SimulateControl (const arma::vec &thetalist, const arma::vec &dthetalist, 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 std::vector< arma::vec > &thetamatd, const std::vector< arma::vec > &dthetamatd, const std::vector< arma::vec > &ddthetamatd, const arma::vec3 &gtilde, const std::vector< arma::mat44 > &Mtildelist, const std::vector< arma::mat66 > &Gtildelist, const double kp, const double ki, const double kd, const double dt, const size_t intRes)
	Simulates the computed torque controller over a given desired trajectory. More...

double	CubicTimeScaling (const double Tf, const double t)
	Computes s(t) for a cubic time scaling. More...

double	QuinticTimeScaling (const double Tf, const double t)
	Computes s(t) for a quintic time scaling. More...

const std::vector< arma::vec >	JointTrajectory (const arma::vec &thetastart, const arma::vec &thetaend, const double Tf, const size_t N, const Method &method)
	Computes a straight-line trajectory in joint space. More...

const std::vector< arma::mat44 >	ScrewTrajectory (const arma::mat44 &Xstart, const arma::mat44 &Xend, const double Tf, const size_t N, const Method &method)
	Computes a trajectory as a list of N SE(3) matrices corresponding to the screw motion about a space screw axis. More...

const std::vector< arma::mat44 >	CartesianTrajectory (const arma::mat44 &Xstart, const arma::mat44 &Xend, const double Tf, const size_t N, const Method &method)
	Computes a trajectory as a list of N SE(3) matrices corresponding to the origin of the end-effector frame following a straight line. More...

constexpr bool	NearZero (const double z)
	Check if a number is close to zero. More...

const arma::vec	Normalize (const arma::vec &vec)
	Normalize a vector to unit length. More...

const arma::mat	JacobianBody (const std::vector< arma::vec6 > &Blist, const arma::vec &thetalist)
	Computes the body Jacobian for an open chain robot. More...

const arma::mat	JacobianSpace (const std::vector< arma::vec6 > &Slist, const arma::vec &thetalist)
	Computes the space Jacobian for an open chain robot. More...

const std::tuple< std::vector< arma::vec >, std::vector< arma::vec > >	SimulateControl (const arma::vec &thetalist, const arma::vec &dthetalist, 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 std::vector< arma::vec > &thetamatd, const std::vector< arma::vec > &dthetamatd, const std::vector< arma::vec > &ddthetamatd, const arma::vec3 &gtilde, const std::vector< arma::mat44 > &Mtildelist, const std::vector< arma::mat66 > &Gtildelist, const double kp, const double ki, const double kd, const double dt, const unsigned int intRes)

Variables
constexpr double	tolerance = 1e-6

Enumeration Type Documentation

◆ Method

enum mr::Method : uint8_t

strong

Trajectory generation method.

Enumerator

Cubic

Quintic

cubic time scaling using 3rd-order polynomial

5th-order polynomial using 5th-order polynomial

Function Documentation

◆ ad()

const arma::mat66 mr::ad ( const arma::vec6 & V )

Calculate the 6x6 matrix [adV] of the given 6-vector.

Parameters

V	A 6-vector spatial velocity

Returns: The corresponding 6x6 matrix [adV]

Used to calculate the Lie bracket [V1, V2] = [adV1]V2

◆ InverseDynamics()

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

◆ NearZero()

constexpr bool mr::NearZero ( const double z )

constexpr

Check if a number is close to zero.

Parameters

x	The number to check

Returns: true if the number is close to zero, false otherwise

◆ Normalize()

const arma::vec mr::Normalize ( const arma::vec & vec )

Normalize a vector to unit length.

Parameters

vec	The vector to normalize

Returns: The normalized vector

◆ SimulateControl()

const std::tuple<std::vector<arma::vec>, std::vector<arma::vec> > mr::SimulateControl	(	const arma::vec &	thetalist,
		const arma::vec &	dthetalist,
		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 std::vector< arma::vec > &	thetamatd,
		const std::vector< arma::vec > &	dthetamatd,
		const std::vector< arma::vec > &	ddthetamatd,
		const arma::vec3 &	gtilde,
		const std::vector< arma::mat44 > &	Mtildelist,
		const std::vector< arma::mat66 > &	Gtildelist,
		const double	kp,
		const double	ki,
		const double	kd,
		const double	dt,
		const unsigned int	intRes
	)

Variable Documentation

◆ tolerance

constexpr double mr::tolerance = 1e-6

constexpr

Enumerations

Functions

Variables

Enumeration Type Documentation

◆ Method

Function Documentation

◆ ad()

◆ InverseDynamics()

◆ NearZero()

◆ Normalize()

◆ SimulateControl()

Variable Documentation

◆ tolerance