Articulated Systems

../_images/anymals.png

ANYmal robots (B and C versions) simulated in RaiSim.

TL;DR

Click the image for vector graphics

../_images/articulatedSystem.png

Introduction

An articulated Systems is a system of multiple bodies connected through joints. There are two types of articulated systems: Kinematic trees and closed-loop systems. Kinematic trees do not contain a loop (a body always has only one parent joint). Consequently, the number of joints is equal to the number of bodies (for floating systems, we assign a floating joint on the root body). RaiSim can only simulate kinematic trees.

Since all bodies have one joint, a body index is always the same as its parent joint’s index. A body refers to a rigid body which is composed of one or more links. All links within a body are connected to each other by a fixed joint.

Creating an instance

Just like any other object, an articulated system is created by the world instance using addArticulatedSystem method. There are three ways to specify the system.

  1. by providing the path to the URDF file (the most recommneded way)

  2. by providing std::string of the URDF text (can be useful when working with Xacro)

  3. by providing a raisim::Child instance. It is an advanced method and not recommnded to beginners.

Note that option 1 and 2 use the same method. You can provide either the path string or the contents string and the class will identify which one is provided.

State Representation

The state of an articulated system can be represented by a generalized state \(\boldsymbol{S}\), which is composed of a generalized coordinate \(\boldsymbol{q}\) and a generalized velocity \(\boldsymbol{u}\). Since we are not constraining their parameterization, in general,

\[\begin{equation} \boldsymbol{u}\neq\dot{\boldsymbol{q}}. \end{equation}\]

A generalized coordinate fully represents the configuration of the articulated system and a generalized velocity fully represents the velocity state of the articulated system.

Every joint has a corresponding generalized coordinate and generalized velocity. A concatenation of all joint generalized coordinates and velocities are the generalized coordinates and velocities of the articulated system, respectively. The order of this concatenation is called joint order. The joint order is determined by the order the joint appears in the URDF unless otherwise it is explicitly given at the instance construction time. The joint order can be accessed through getMovableJointNames(). Note the keyword “movable”. The fixed joints contribute to neither the generalized coordinate nor the generalized velocity. Only movable joints do (with one exception metioned below).

The joint order starts with the root body which is the first body of the articulated system. For floating-base systems, the root body is the floating base. For fixed-base systems, the root body is the one rigidly attached to the wolrd. Even though the fixed base cannot move physically, users can move them using setBaseOrientation and setBasePosition. So getMovableJointNames() method will return the fixed base name and the fixed base joint is a part of the joint order.

The following example illustrates how the generalized coordinates and velocities are defined.

To set the state of the system, the following methods can be used

  • setGeneralizedCoordinate

  • setGeneralizedVelocity

  • setState

To obtain the state of the system, the following methods can be used

  • getGeneralizedCoordinate

  • getGeneralizedVelocity

  • getState

The dimensions of each vector can be obtained respectively by

  • getGeneralizedCoordinateDim

  • getDOF or getGeneralizedVelocityDim.

These two methods are identical

Joints

Here are the available joints in RaiSim.

Joint Properties (\(|\cdot|\) is a symbol for dimension size (i.e., cardinality))

Fixed

Floating

Revolute

Prismatic

Spherical

\(|\boldsymbol{u}|\)

0

6

1

1

3

\(|\boldsymbol{q}|\)

0

7

1

1

4

Velocity

\(m/s\), \(rad/s\)

\(rad/s\)

\(m/s\)

\(rad/s\)

Position

\(m\), \(rad\)

\(rad\)

\(m\)

\(rad\)

Force

\(N\), \(Nm\)

\(Nm\)

\(N\)

\(Nm\)

The generalized coordinates/velocities of a joint are expressed in the joint frame and with respect to the parent body. Joint frame is the frame attached to every joint and fixed to the parent body. Parent body is the one closer to the root body among the two bodies connected via the joint. Note that the angular velocity of a floating base is also expressed in the parent frame (which is the world frame). Other libraries (e.g., RBLD) might have a different convention and a special care has to be taken in conversions.

URDF convention

RaiSim uses a modified URDF protocol to define an articulated system. URDF files following the original convention can be read in RaiSim. However, since RaiSim offers more functionalities, a RaiSim URDF might not be read by other libraries following the original URDF convention.

The modifications are as follows:

  • Capsule geom is available for both collision objects and visual objects (with the keyword “capsule”). The geom is defined by “height” and “radius” keyword. The height represents the distance between the two center points of the spheres.

  • A <joint>/<dynamics> tag can have three more attributes: rotor_inertia, spring_mount and stiffness.

Here is an example joint with the raisim tags

<joint name="link1Tolink2" type="spherical">
    <parent link="link1"/>
    <child link="link2"/>
    <origin xyz="0 0 -0.24"/>
    <axis xyz="0 1 0"/>
    <dynamics rotor_inertia="0.0001" spring_mount="0.70710678118 0 0.70710678118 0" stiffness="500.0" damping="3."/>
</joint>

Rotor_inertia in Raisim approximately simulates the rotor inertia of the motor (but missing the resulting gyroscopic effect, which is often neglegible).

It is added to the diagonal elements of the mass matrix. It is common way to include the inertial effect of the rotor. You can also override it in C++ using setRotorInertia(). Since RaiSim does not know the gear ratio, you have to multiply the rotor inertia by the square of the gear ratio yourself. In other words, the value is the reflected rotor inertia observed at the joint.

And two preprocessor features (that are also available in the raisim world configuration file) are available for the URDF template.

  • You can specify a variable in a form of “@@Robot_Height”. The value of this variable can be specified at the run timeusing ‘’std::unordered_map’’ and the corresponding factory method in ‘’raisim::World::.

  • You can specify an equation instead of a variable. For example, {@@Robot_Height*@@Robot_Width*2}.

The preprocessor example can be found in examples/src/server/trackedRobotAndTemplatedURDF.cpp and the corresponding URDF template in rsc/templatedTrackedRobot/trackedTemplate.urdf.

In RaiSim, each body of an articulated system has a set of collision bodies and visual objects. Collision bodies contain a collision object of one of the following shapes: mesh, sphere, box, cylinder, capsule. Visual objects just store specifications for visualization and the actual visualzation happens in a visualizer (e.g., raisimOgre) For details, check the URDF protocol.

Kinematics

Frames

A position and velocity of a specific point on a body of an articulated system can be obtained by attaching a frame. Frames are rigidly attached to a body of the system and has a constant position and orientation (w.r.t. parent frame). It is the most recommended way to get kinematics information of a point of an articulated system in RaiSim.

All joints have a frame attached and their names are the same as the joint name. To create a custom frame, a fixed frame can be defined at the point of the interest. A dummy link with zero inertia and zero mass must be added on one side of the fixed joint to complete the kinematic tree.

A frame can be locally stored as an index in the user code. For e.g.,

#include “raisim/World.hpp”

int main() {
  raisim::World world;
  auto anymal = world.addArticulatedSystem(PATH_TO_URDF);
  auto footFrameIndex = anymal->getFrameIdxByName("foot_joint"); // the URDF has a joint named "foot_joint"
  raisim::Vec<3> footPosition, footVelocity, footAngularVelocity;
  raisim::Mat<3,3> footOrientation;
  anymal->getFramePosition(footFrameIndex, footPosition);
  anymal->getFrameOrientation(footFrameIndex, footOrientation);
  anymal->getFrameVelocity(footFrameIndex, footVelocity);
  anymal->getFrameAngularVelocity(footFrameIndex, footAngularVelocity);
}

You can also store a Frame reference. For e.g., you can replace getFrameIdxByName by getFrameByName in the above example. In this way, you can access the internal variables and even modify them. Modifying the frames do not affect the joints. Frames are instantiated during initialization of the articulated system instance and affect neither kinematics nor dynamics of the system.

Jacobians

Jacobians of a point in RaiSim satisfy the following equation:

\[\begin{equation} \boldsymbol{J}\boldsymbol{u} = \boldsymbol{v} \end{equation}\]

where \(\boldsymbol{v}\) represents the linear velocity of the associated point. If a rotational Jacobian is used, the right-hand side changes to a rotational velocity expressed in the world frame.

To get the Jacobians associated with the linear velocity, the following methods are used

  • getSparseJacobian

  • getDenseJacobian – this method only fills non-zero values. The matrix should be initialized to a zero matrix of an appropriate size.

To get the rotational Jacobians, the following methods are used

  • getSparseRotationalJacobian

  • getDenseRotationalJacobian – this method only fills non-zero values. The matrix should be initialized to a zero matrix of an appropriate size.

The main Jacobian class in RaiSim is raisim::SparseJacobian. RaiSim uses only sparse Jacobians as it is more memory-friendly. Note that only the joints between the child body and the root body affect the motion of the point.

The class raisim::SparseJacobian has a member idx which stores the indicies of columns whose values are non-zero. The member v stores the Jacobian except the zero columns. In other words, ith column of v corresponds to idx[i] generalized velocity dimension.

Dynamics

All force and torque acting on the system can be represented as a single vector in the generalized velocity space. This representation is called generalized force \(\boldsymbol{\tau}\). Just like in a Cartesian coordiate (i.e., x, y, z axes), the power exerted by an articulated system is computed as a dot product of generalized force and generalized velocity (i.e., \(\boldsymbol{u}\cdot\boldsymbol{\tau}\)).

We can also combine the mass and inertia of the whole articulated system and represent them in a single matrix. This matrix is called mass matrix or inertia matrix and denoted by \(\boldsymbol{M}\). A mass matrix represents how much the articulated system resists change in generalized velocities. Naively speaking, a large mass matrix means that the articulated system experiences a low velocity change for a given generalized force.

The total kinetic energy of the system is computed as \(\frac{1}{2}\boldsymbol{u}^T\boldsymbol{M}\boldsymbol{u}\). This quantity can be obtained by getKineticEnergy().

The total potential energy due to the gravity is a sum of \(mgh\) for all bodies. This quantity can be obtained by getPotentialEnergy(). Note that the gravity has to be specified since only the world has the gravity vector.

The equation of motion of an articulated system is shown below:

\[\begin{equation} \boldsymbol{\tau} = \boldsymbol{M}(\boldsymbol{q})\dot{\boldsymbol{u}} + \boldsymbol{h}(\boldsymbol{q}, \boldsymbol{u}). \end{equation}\]

Here \(\boldsymbol{h}\) is called a non-linear term. There are three sources of force that contributes to the non-linear term: gravity, coriolis, and centrifugal force. It is rarely useful to compute the gravity contribution to the nonlinear term alone. However, if it is needed, the easiest way is to make the same robot in another world with zero velocity. If the generalized velocity is zero, the coriolis and centrifugal contributions are zero.

The following methods are used to obtain dynamic quantities

  • getMassMatrix()

  • getNonlinearities()

  • getInverseMassMatrix()

PD Controller

When naively implemented, a PD controller can often make a robot unstable. However, this is often not so bad for robotics since this instability is also present in the real system (discrete-time control system).

For other applications like animation and graphics, it is often desirable to have a stable PD controller when a user wants to keep the time step small. Therefore, this PD controller exploits a more stable integration scheme and can have much smaller time step than a naive implementation.

This PD controller does not respect the actuation limits of the robot. It uses an implicit integration scheme and we do not even compute the actual torque that is applied to the joints.

To use this PD controller, you have to set the desirable control gains first

Eigen::VectorXd pGain(robot->getDOF()), dGain(robot->getDOF());
pGain<< ...; // set your proportional gain values here
dGain<< ...; // set your differential gain values here
robot->setPdGains(pGain, dGain);

Note that the dimension of the pGain vector is the same as that of the generalized velocity NOT that of the coordinate.

Finally, the target position and the velocity can set as below

Eigen::VectorXd pTarget(robot->getGeneralizedCoordinateDim()), vTarget(robot->getDOF());
pTarget<< ...; // set your position target
vTarget<< ...; // set your velocity target
robot->setPdTarget(pTarget, vTarget);

Here, the dimension of the pTarget vector is the same as that of the generalized coordinate NOT that of the velocity. This is confusing and might seem inconsistent. However, this is a valid convention. The only reason that the two dimensions differ is quaternions. The quaternion target is represented by a quaternion whereas the virtual spring stiffness between the two orientations can be represented by a 3D vector, which is composed of motions in each angular velocity components.

A feedforward force term can be added by setGeneralizedForce() if desired. This term is set to zero by default. Note that this value is stored in the class instance and does not change unless the user specifies it so. If this feedforward force should be applied for a single time step, it should be set to zero in the subsequent control loop (after integrate() call of the world).

The theory of the implemented PD controller can be found in chapter 1.2 of this article. This document is only for advanced users and it is not necessary to use RaiSim.

Integration Steps

Integration of an articulated systems is performed in two stages: integrate1 and integrate2

The following steps are performed in integrate1

  1. If the time step is changed, update the damping of the mass matrix (which reflects effective inertial increase due to springs, dampers and PD gains)

  2. Update positions of the collision bodies

  3. Detect collisions (called by the world instance)

  4. The world assigns contacts on each object and computes the contact normal

  5. Compute the mass matrix, nonlinear term and inverse inertia matrix

  6. Compute (Sparse) Jacobians of contacts

After this step, all kinematic/dynamic proerpties are computed at this stage. Users can access them if they are necessary for the controller. Next, integrate2 computes the rest of the simulation.

  1. Compute contact Properties

  2. Compute PD controller (if used), add it to the feedforward force and bound it by the limits

  3. Compute generalized forces due to springs and external forces/torques

  4. Contact solver (called by the world instance)

  5. Integrate the velocity

  6. Integrate the position (in a semi-implicit way)

Get and Modify Robot Description in code

RaiSim allows users modify most of the robot parameters freely in code. This allows users to create randomized robot model, which might be useful for AI applications (i.e., dynamic randomization). Note that a random model might be kinematically and dynamically unrealistic. For example, joints can be locked by collision bodies. In such cases, simulation cannot be performed reliably and it is advised to carefully check randomly generated robot models.

Here is a list of modifiable kinematic/dynamic parameters.

  • Joint Position (relative to the parent joint) Expressed in the Parent Frame

getJointPos_P method returns (a non-const reference to) a std::vector of position vectors from the parent joint to the child joint expressed in the respective parent joint frames. This should be changed with care since it can result in unrealistic collision geometry. This method does not change the position of the end-effector with respect to its parent as the position of the last link is defined by the collision body position, not by the joint position. The elements are ordered by the joint indicies.

  • Joint Axis in the Parent Frame

getJointAxis_P method returns (a non-const reference to) a std::vector of joint axes expressed in the respective parent joint frame. This method should also be changed with care. The elements are ordered by the joint indicies.

  • Mass of the Links

getMass method returns (a non-const reference to) a std::vector of link masses. IMPORTANT! You must call :code:`updateMassInfo` after changing mass values. The elements are ordered by the body indicies (which is the same as the joint indicies in RaiSim).

  • Center of Mass Position

getBodyCOM_B method returns (a non-const reference to) a std::vector of the COM of the bodies. The elements are ordered by the body indices.

  • Link Inertia

getInertia method returns (a non-const reference to) a std::vector of link inertia. The elements are ordered by the body indicies.

  • Collision Bodies

getCollisionBodies method returns (a non-const reference to) a std::vector of the collision bodies. This vector contains all collision bodies associated with the articulated system.

getCollisionBody method returns a specific collision body instead. All collision bodies are named “LINK_NAME” + “/INDEX”. For example, the 2nd collision body of a link named “FOOT” is named “FOOT/1” (1 because the index starts from 0).

The collision bodies is a class that contains position/orientation offset from the parent joint frame, name, parent body index, and ODE collision pointer (dGeomID, retrieved using getCollisionObject). The collision geom can be modified using ODE methods (ODE manual). Users can also modify the material of the collision body. This material affects the contact dynamics.

Apply External Forces/torques

The following two methods are used to apply external force and torque respectively

  • setExternalForce

  • setExternalTorque

Collision

Apart from the collision mask and collision group set in the world, users can also disable a collision between a certain pair of the links with ignoreCollisionBetween.

Types of Indicies

ArticulatedSystem class contains multiple types of indicies. To query a specific quantity, you have to provide an index of the right type. Here are the types of indicies in Articulated Systems

  • Body/Joint Index: All fixed bodies are combined to a single movable body. Each movable body has a unique body index. Because there is a movable joint associated with a movable body, there is a 1-to-1 mapping between the joints and the bodies and they share the same index. For a fixed-base system, the first body rigidly fixed to the world is body-0. For a floating-base system, the floating base is body-0.

  • Generalized Velocity (DOF) Index: All joints are mapped to a specific set of generalized velocity indicies.

  • Generalized Coordinate Index:

  • Frame Index:

Conversions Between Indicies

  • A body index to a generalized velocity index: ArticulatedSystem::getMappingFromBodyIndexToGeneralizedVelocityIndex()

  • A body index to a generalized coordinate index: ArticulatedSystem::getMappingFromBodyIndexToGeneralizedCoordinateIndex()

API

class raisim::ArticulatedSystem : public raisim::Object

Public Functions

inline const raisim::VecDyn &getGeneralizedCoordinate() const
Returns

generalized coordinate of the system

inline const raisim::VecDyn &getGeneralizedVelocity() const
Returns

generalized velocity of the system

void getBaseOrientation(raisim::Vec<4> &quaternion) const
Parameters

quaternion[out] orientation of base

inline void getBaseOrientation(raisim::Mat<3, 3> &rotataionMatrix) const
Parameters

rotataionMatrix[out] orientation of base

inline const raisim::Mat<3, 3> &getBaseOrientation() const
Returns

orientation of base

inline void getBasePosition(raisim::Vec<3> &position) const
Parameters

position[out] position of base

inline raisim::Vec<3> getBasePosition() const
Returns

position of base

void updateKinematics()

unnecessary to call this function if you are simulating your system. integrate1 calls this function Call this function if you want to get kinematic properties but you don’t want to integrate.

inline void setGeneralizedCoordinate(const Eigen::VectorXd &jointState)

set gc of each joint in order

Parameters

jointState[in] generalized coordinate

inline void setGeneralizedCoordinate(const raisim::VecDyn &jointState)

set gc of each joint in order

Parameters

jointState[in] generalized coordinate

inline void setGeneralizedVelocity(const Eigen::VectorXd &jointVel)

set the generalized velocity

Parameters

jointVel[in] the generalized velocity

inline void setGeneralizedVelocity(const raisim::VecDyn &jointVel)

set the generalized velocity

Parameters

jointVel[in] the generalized velocity

void setGeneralizedCoordinate(std::initializer_list<double> jointState)

set the generalized coordinsate of each joint in order.

Parameters

jointState[in] the generalized coordinate

void setGeneralizedVelocity(std::initializer_list<double> jointVel)

set the generalized velocity of each joint in order

Parameters

jointVel[in] the generalized velocity

void setGeneralizedForce(std::initializer_list<double> tau)

This is feedforward generalized force. In the PD control mode, this differs from the actual generalizedForce the dimension should be the same as dof.

Parameters

tau[in] the generalized force. If the built-in PD controller is active, this force is added to the generalized force from the PD controller

inline void setGeneralizedForce(const raisim::VecDyn &tau)

This is feedforward generalized force. In the PD control mode, this differs from the actual generalizedForce the dimension should be the same as dof.

Parameters

tau[in] the generalized force. If the built-in PD controller is active, this force is added to the generalized force from the PD controller

inline void setGeneralizedForce(const Eigen::VectorXd &tau)

This is feedforward generalized force. In the PD control mode, this differs from the actual generalizedForce the dimension should be the same as dof.

Parameters

tau[in] the generalized force. If the built-in PD controller is active, this force is added to the generalized force from the PD controller

inline void getState(Eigen::VectorXd &genco, Eigen::VectorXd &genvel) const

get both the generalized coordinate and the generalized velocity

Parameters
  • genco[out] the generalized coordinate

  • genvel[out] the generalized velocity

inline void getState(VecDyn &genco, VecDyn &genvel) const

get both the generalized coordinate and the generalized velocity

Parameters
  • genco[out] the generalized coordinate

  • genvel[out] the generalized velocity

inline void setState(const Eigen::VectorXd &genco, const Eigen::VectorXd &genvel)

set both the generalized coordinate and the generalized velocity. This updates the kinematics and removes previously computed contact points

Parameters
  • genco[in] the generalized coordinate

  • genvel[in] the generalized velocity

inline VecDyn getGeneralizedForce() const

Generalized user-set gen force (using setGeneralizedForce()). This method a small error when the built-in PD controller is used. The PD controller is implicit (using a continuous, linear model) so we cannot get the true gen force. But if you set the time step small enough, the difference is negligible.

Returns

the generalized force

inline const VecDyn &getFeedForwardGeneralizedForce() const

get the feedfoward generalized force (which is set by the user)

Returns

the feedforward generalized force

inline const MatDyn &getMassMatrix()

get the mass matrix

Returns

the mass matrix. Check Object/ArticulatedSystem section in the manual

inline const VecDyn &getNonlinearities(const Vec<3> &gravity)

get the coriolis and the gravitational term

Parameters

gravity[in] gravitational acceleration. You should get this value from the world.getGravity();

Returns

the coriolis and the gravitational term. Check Object/ArticulatedSystem section in the manual

inline const MatDyn &getInverseMassMatrix()

get the inverse mass matrix. Note that this is actually damped inverse. It contains the effect of damping and the spring effects due to the implicit integration. YOU MUST CALL getMassMatrix FIRST BEFORE CALLING THIS METHOD.

Returns

the inverse mass matrix. Check Object/ArticulatedSystem section in the manual

inline const std::vector<raisim::Vec<3>> &getCompositeCOM() const

get the center of mass of a composite body containing body i and all its children. if you want the COM of the whole robot, just take the first element This only works if you have called getMassMatrix() with the current state

Returns

the center of mass of the composite body

inline Vec<3> getCOM() const

get the center of mass of the whole system

Returns

the center of mass of the system

inline const std::vector<raisim::Mat<3, 3>> &getCompositeInertia() const

get the current composite inertia of a composite body containing body i and all its children

Returns

the inertia of the composite system

inline const std::vector<double> &getCompositeMass() const

get the current composite mass of a composite body containing body i and all its children

Returns

get the composite mass

inline Vec<3> getLinearMomentum() const

linear momentum of the whole system

Returns

momentum

inline const VecDyn &getGeneralizedMomentum() const

returns the generalized momentum which is M * u It is already computed in “integrate1()” so you don’t have to compute again.

Returns

the generalized momentum

double getEnergy(const Vec<3> &gravity)
Parameters

gravity[in] gravitational acceleration

Returns

the sum of potential/kinetic energy given the gravitational acceleration

double getKineticEnergy()
Returns

the kinetic energy.

double getPotentialEnergy(const Vec<3> &gravity) const
Parameters

gravity[in] gravitational acceleration

Returns

the potential energy (relative to zero height) given the gravity vector

void getAngularMomentum(const Vec<3> &referencePoint, Vec<3> &angularMomentum) const
Parameters
  • referencePoint[in] the reference point about which the angular momentum is computed

  • angularMomentum[in] angular momentum about the reference point

void printOutBodyNamesInOrder() const

bodies here means moving bodies. Fixed bodies are optimized out

void printOutMovableJointNamesInOrder() const

print out movable joint names in order

void printOutFrameNamesInOrder() const

frames are attached to every joint coordinate

inline const std::vector<std::string> &getMovableJointNames() const

getMovableJointNames. Note! the order doesn’t correspond to dof since there are joints with multiple dof’s

Returns

movable joint names in the joint order.

virtual void getPosition(size_t bodyIdx, const Vec<3> &point_B, Vec<3> &point_W) const final
Parameters
  • bodyIdx[in] The body which contains the point, can be retrieved by getBodyIdx()

  • point_B[in] The position of the point in the body frame

  • point_W[out] The position of the point in the world frame

Returns

position in the world frame of a point defined in a joint frame

inline CoordinateFrame &getFrameByName(const std::string &nm)

Refer to Object/ArticulatedSystem/Kinematics/Frame in the manual for details

Parameters

nm[in] name of the frame

Returns

the coordinate frame of the given name

inline CoordinateFrame &getFrameByIdx(size_t idx)

Refer to Object/ArticulatedSystem/Kinematics/Frame in the manual for details

Parameters

idx[in] index of the frame

Returns

the coordinate frame of the given index

size_t getFrameIdxByName(const std::string &nm) const

Refer to Object/ArticulatedSystem/Kinematics/Frame in the manual for details The frame can be retrieved as as->getFrames[index]. This way is more efficient than above methods that use the frame name

Parameters

nm[in] name of the frame

Returns

the index of the coordinate frame of the given index. Returns size_t(-1) if it doesn’t exist

inline std::vector<CoordinateFrame> &getFrames()

Refer to Object/ArticulatedSystem/Kinematics/Frame in the manual for details The frame can be retrieved as as->getFrames[index]. This way is more efficient than above methods that use the frame name

Returns

a vector of the coordinate frames

void getFramePosition(size_t frameId, Vec<3> &point_W) const
Parameters
  • frameId[in] the frame id which can be obtained by getFrameIdxByName()

  • point_W[out] the position of the frame expressed in the world frame

void getFrameOrientation(size_t frameId, Mat<3, 3> &orientation_W) const
Parameters
  • frameId[in] the frame id which can be obtained by getFrameIdxByName()

  • orientation_W[out] the position of the frame relative to the world frame

void getFrameVelocity(size_t frameId, Vec<3> &vel_W) const
Parameters
  • frameId[in] the frame id which can be obtained by getFrameIdxByName()

  • vel_W[out] the linear velocity of the frame expressed in the world frame

void getFrameAngularVelocity(size_t frameId, Vec<3> &angVel_W) const
Parameters
  • frameId[in] the frame id which can be obtained by getFrameIdxByName()

  • angVel_W[out] the angular velocity of the frame expressed in the world frame

inline void getFramePosition(const std::string &frameName, Vec<3> &point_W) const
Parameters
  • frameName[in] the frame name (defined in the urdf)

  • point_W[out] the position of the frame expressed in the world frame

inline void getFrameOrientation(const std::string &frameName, Mat<3, 3> &orientation_W) const
Parameters
  • frameName[in] the frame name (defined in the urdf)

  • orientation_W[out] the orientation of the frame relative to the world frame

inline void getFrameVelocity(const std::string &frameName, Vec<3> &vel_W) const
Parameters
  • frameName[in] the frame name (defined in the urdf)

  • vel_W[out] the linear velocity of the frame expressed in the world frame

inline void getFrameAngularVelocity(const std::string &frameName, Vec<3> &angVel_W) const
Parameters
  • frameName[in] the frame name (defined in the urdf)

  • angVel_W[out] the angular velocity of the frame relative to the world frame

void getFramePosition(const CoordinateFrame &frame, Vec<3> &point_W) const
Parameters
  • frame[in] custom frame defined by the user

  • point_W[out] the position of the frame relative to the world frame

void getFrameOrientation(const CoordinateFrame &frame, Mat<3, 3> &orientation_W) const
Parameters
  • frame[in] custom frame defined by the user

  • orientation_W[out] the orientation of the frame relative to the world frame

void getFrameVelocity(const CoordinateFrame &frame, Vec<3> &vel_W) const
Parameters
  • frame[in] custom frame defined by the user

  • vel_W[out] the linear velocity of the frame expressed to the world frame

void getFrameAngularVelocity(const CoordinateFrame &frame, Vec<3> &angVel_W) const
Parameters
  • frame[in] custom frame defined by the user

  • angVel_W[out] the angular velocity of the frame expressed to the world frame

inline virtual void getPosition(size_t bodyIdx, Vec<3> &pos_w) const final
Parameters
  • bodyIdx[in] the body index. Note that body index and the joint index are the same because every body has one parent joint. It can be retrieved by getBodyIdx()

  • pos_w[out] the position of the joint (after its own joint transformation)

void getPositionInBodyCoordinate(size_t bodyIdx, const Vec<3> &pos_W, Vec<3> &pos_B)
Parameters
  • bodyIdx[in] the body index. Note that body index and the joint index are the same because every body has one parent joint. It can be retrieved by getBodyIdx()

  • pos_W[in] the position in the world coordinate. This position does not have to be physically on the body.

  • pos_B[out] the position in the body frame

inline virtual void getOrientation(size_t bodyIdx, Mat<3, 3> &rot) const final
Parameters
  • bodyIdx[in] the body index. Note that body index and the joint index are the same because every body has one parent joint. It can be retrieved by getBodyIdx()

  • rot[out] the orientation of the joint (after its own joint transformation)

inline virtual void getVelocity(size_t bodyIdx, Vec<3> &vel_w) const final
Parameters
  • bodyIdx[in] the body index. Note that body index and the joint index are the same because every body has one parent joint. It can be retrieved by getBodyIdx()

  • vel_w[out] the linear velocity of the joint (after its own joint transformation)

inline void getAngularVelocity(size_t bodyIdx, Vec<3> &angVel_w) const
Parameters
  • bodyIdx[in] the body index. Note that body index and the joint index are the same because every body has one parent joint. It can be retrieved by getBodyIdx()

  • angVel_w[out] the angular velocity of the joint (after its own joint transformation)

void getSparseJacobian(size_t bodyIdx, const Vec<3> &point_W, SparseJacobian &jaco) const
Parameters
  • bodyIdx[in] the body index. Note that body index and the joint index are the same because every body has one parent joint. It can be retrieved by getBodyIdx()

  • point_W[in] the point expressed in the world frame. If you want to use a point expressed in the body frame, use getDenseFrameJacobian()

  • jaco[out] the positional Jacobian. v = J * u. v is the linear velocity expressed in the world frame and u is the generalized velocity

void getSparseRotationalJacobian(size_t bodyIdx, SparseJacobian &jaco) const
Parameters
  • bodyIdx[in] the body index. Note that body index and the joint index are the same because every body has one parent joint. It can be retrieved by getBodyIdx()

  • jaco[out] the rotational Jacobian. omega = J * u. omgea is the angular velocity expressed in the world frame and u is the generalized velocity

inline void getDenseJacobian(size_t bodyIdx, const Vec<3> &point_W, Eigen::MatrixXd &jaco) const

This method only fills out non-zero elements. Make sure that the jaco is setZero() once in the initialization!

Parameters
  • bodyIdx[in] the body index. Note that body index and the joint index are the same because every body has one parent joint

  • point_W[in] the point expressed in the world frame. If you want to use a point expressed in the body frame, use getDenseFrameJacobian()

  • jaco[out] the dense positional Jacobian

inline void getDenseRotationalJacobian(size_t bodyIdx, Eigen::MatrixXd &jaco) const

This method only fills out non-zero elements. Make sure that the jaco is setZero() once in the initialization!

Parameters
  • bodyIdx[in] the body index. it can be retrieved by getBodyIdx()

  • jaco[out] the dense rotational Jacobian

inline void getDenseFrameJacobian(size_t frameIdx, Eigen::MatrixXd &jaco) const

This method only fills out non-zero elements. Make sure that the jaco is setZero() once in the initialization!

Parameters
  • frameIdx[in] the frame index. it can be retrieved by getFrameIdxByName()

  • jaco[out] the dense positional Jacobian

inline void getDenseFrameJacobian(const std::string &frameName, Eigen::MatrixXd &jaco) const

This method only fills out non-zero elements. Make sure that the jaco is setZero() once in the initialization!

Parameters
  • frameName[in] the frame name. (defined in the URDF)

  • jaco[out] the dense positional Jacobian

inline void getDenseFrameRotationalJacobian(size_t frameIdx, Eigen::MatrixXd &jaco) const

This method only fills out non-zero elements. Make sure that the jaco is setZero() once in the initialization!

Parameters
  • frameIdx[in] the frame index. it can be retrieved by getFrameIdxByName()

  • jaco[out] the dense rotational Jacobian

inline void getDenseFrameRotationalJacobian(const std::string &frameName, Eigen::MatrixXd &jaco) const

This method only fills out non-zero elements. Make sure that the jaco is setZero() once in the initialization!

Parameters
  • frameName[in] the frame name. (defined in the URDF)

  • jaco[out] the dense rotational Jacobian

void getVelocity(const SparseJacobian &jaco, Vec<3> &pointVel) const
Parameters
  • jaco[in] the Jacobian associated with the point of interest

  • pointVel[out] the velocity of the point expressed in the world frame

void getVelocity(size_t bodyIdx, const Vec<3> &posInBodyFrame, Vec<3> &pointVel) const
Parameters
  • bodyIdx[in] the body index. it can be retrieved by getBodyIdx()

  • posInBodyFrame[in] the position of the point of interest expressed in the body frame

  • pointVel[out] the velocity of the point expressed in the world frame

size_t getBodyIdx(const std::string &nm) const

returns the index of the body

Parameters

nm[in] name of the body. The body name is the name of the movable link of the body

Returns

the index of the body. Returns size_t(-1) if the body doesn’t exist.

size_t getDOF() const
Returns

the degrees of freedom

size_t getGeneralizedVelocityDim() const
Returns

the dimension of generalized velocity (do the same thing with getDOF)

size_t getGeneralizedCoordinateDim() const
Returns

the dimension of generalized coordinate

inline void getBodyPose(size_t bodyIdx, Mat<3, 3> &orientation, Vec<3> &position) const

The body pose is the pose of its parent joint (after its joint transformation)

Parameters
  • bodyIdx[in] the body index. it can be retrieved by getBodyIdx()

  • orientation[out] the orientation of the body

  • position[out] the position of the body

inline void getBodyPosition(size_t bodyIdx, Vec<3> &position) const

The body position is the position of its parent joint (after its joint transformation)

Parameters
  • bodyIdx[in] the body index. it can be retrieved by getBodyIdx()

  • position[out] the position of the body

inline void getBodyOrientation(size_t bodyIdx, Mat<3, 3> &orientation) const

The body orientation is the orientation of its parent joint (after its joint transformation)

Parameters
  • bodyIdx[in] the body index. it can be retrieved by getBodyIdx()

  • orientation[out] the orientation of the body

inline std::vector<raisim::Vec<3>> &getJointPos_P()

The following 5 methods can be used to directly modify dynamic/kinematic properties of the robot. They are made for dynamic randomization. Use them with caution since they will change the the model permenantly. After you change the dynamic properties, call “void updateMassInfo()” to update some precomputed dynamic properties

Returns

a reference to joint position relative to its parent, expressed in the parent frame.

inline std::vector<raisim::Mat<3, 3>> &getJointOrientation_P()
Returns

a reference to joint orientation relative to its parent.

inline std::vector<raisim::Vec<3>> &getJointAxis_P()
Returns

a reference to joint axis relative to its parent, expressed in the parent frame.

inline const raisim::Vec<3> &getJointAxis(size_t idx) const
Returns

a reference to joint axis expressed in the world frame.

inline std::vector<double> &getMass()

You MUST call updateMassInfo() after you change the mass

Returns

a reference to mass of each body.

inline std::vector<raisim::Mat<3, 3>> &getInertia()
Returns

a reference to inertia of each body.

inline std::vector<raisim::Vec<3>> &getBodyCOM_B()
Returns

a reference to the position of the center of the mass of each body in the body frame.

inline std::vector<raisim::Vec<3>> &getBodyCOM_W()
Returns

a reference to the position of the center of the mass of each body in the world frame.

inline raisim::CollisionSet &getCollisionBodies()
Returns

a reference to the collision bodies. Position and orientation can be set dynamically

inline raisim::CollisionDefinition &getCollisionBody(const std::string &name)
Parameters

name – collision body name which is “LINK_NAME” + “/” + “COLLISION_NUMBER”. For example, the first collision body of the link “base” is named as “base/0”

Returns

a reference to the collision bodies. Position and orientation can be set dynamically

void updateMassInfo()

This method updates the precomputed composite mass. Call this method after you change link mass. This also updates the center of mass without integration

inline virtual double getMass(size_t bodyIdx) const final
Parameters

bodyIdx[in] the body index. it can be retrieved by getBodyIdx()

Returns

mass of the body

inline void setMass(size_t bodyIdx, double value)

set body mass. It is indexed for each body, not for individual link. Check this link (https://raisim.com/sections/ArticulatedSystem.html#introduction) to understand the difference between a link and a body

inline double getTotalMass() const
Returns

the total mass of the system.

virtual void setExternalForce(size_t bodyIdx, const Vec<3> &force) final

set external forces or torques expressed in the world frame acting on the COM of the body. The external force is applied for a single time step only. You have to apply the force for every time step if you want persistent force

Parameters
  • bodyIdx[in] the body index. it can be retrieved by getBodyIdx()

  • force[in] force applied to the body (at the center of mass)

void setExternalForce(size_t bodyIdx, Frame frameOfForce, const Vec<3> &force, Frame frameOfPos, const Vec<3> &pos)

set external force acting on the point specified The external force is applied for a single time step only. You have to apply the force for every time step if you want persistent force

Parameters
  • bodyIdx[in] the body index. it can be retrieved by getBodyIdx()

  • frameOfForce[in] the frame in which the force is expressed. Options: Frame::WORLD_FRAME, Frame::PARENT_FRAME or Frame::BODY_FRAME

  • force[in] the applied force

  • frameOfPos[in] the frame in which the position vector is expressed. Options: Frame::WORLD_FRAME, Frame::PARENT_FRAME or Frame::BODY_FRAME

  • pos[in] position at which the force is applied

inline virtual void setExternalForce(size_t bodyIdx, const Vec<3> &pos, const Vec<3> &force) final

set external force (expressed in the world frame) acting on the point (expressed in the body frame) specified The external force is applied for a single time step only. You have to apply the force for every time step if you want persistent force

Parameters
  • bodyIdx[in] the body index. it can be retrieved by getBodyIdx()

  • force[in] the applied force

  • pos[in] position at which the force is applied

inline void setExternalForce(const std::string &frame_name, const Vec<3> &force)

set external force (expressed in the world frame) acting on the point specified by the frame The external force is applied for a single time step only. You have to apply the force for every time step if you want persistent force

Parameters
  • frame_name[in] the name of the frame where you want to applied the force. The force is applied to the origin of the frame, on the body where the frame is attached to.

  • force[in] the applied force in the world frame

virtual void setExternalTorque(size_t bodyIdx, const Vec<3> &torque_in_world_frame) final

set external torque. The external torque is applied for a single time step only. You have to apply the force for every time step if you want persistent torque

Parameters
  • bodyIdx[in] the body index. it can be retrieved by getBodyIdx()

  • torque_in_world_frame[in] the applied torque expressed in the world frame

virtual void getContactPointVel(size_t contactId, Vec<3> &vel) const final

returns the contact point velocity. The contactId is the order in the vector from Object::getContacts()

Parameters
  • contactId[in] index of the contact vector which can be obtained by getContacts()

  • vel[out] the contact point velocity

inline void setControlMode(ControlMode::Type mode)
Parameters

mode[in] control mode. Can be either ControlMode::FORCE_AND_TORQUE or ControlMode::PD_PLUS_FEEDFORWARD_TORQUE

inline ControlMode::Type getControlMode() const
Returns

control mode. Can be either ControlMode::FORCE_AND_TORQUE or ControlMode::PD_PLUS_FEEDFORWARD_TORQUE

inline void setPdTarget(const Eigen::VectorXd &posTarget, const Eigen::VectorXd &velTarget)

set PD targets.

Parameters
  • posTarget[in] position target

  • velTarget[in] velocity target

inline void getPdTarget(Eigen::VectorXd &posTarget, Eigen::VectorXd &velTarget)

get PD targets.

Parameters
  • posTarget[out] position target

  • velTarget[out] velocity target

inline void setPdTarget(const raisim::VecDyn &posTarget, const raisim::VecDyn &velTarget)

set PD targets.

Parameters
template<class T>
inline void setPTarget(const T &posTarget)

set P targets.

Parameters

posTarget[in] position target (dimension == getGeneralizedCoordinateDim())

template<class T>
inline void setDTarget(const T &velTarget)

set D targets.

Parameters

velTarget[in] velocity target (dimension == getDOF())

inline void setPdGains(const Eigen::VectorXd &pgain, const Eigen::VectorXd &dgain)

set PD gains.

Parameters
  • pgain[in] position gain (dimension == getDOF())

  • dgain[in] velocity gain (dimension == getDOF())

inline void getPdGains(Eigen::VectorXd &pgain, Eigen::VectorXd &dgain)

get PD gains.

Parameters
  • pgain[out] position gain (dimension == getDOF())

  • dgain[out] velocity gain (dimension == getDOF())

inline void setPdGains(const raisim::VecDyn &pgain, const raisim::VecDyn &dgain)

set PD gains.

Parameters
  • pgain[in] position gain (dimension == getDOF())

  • dgain[in] velocity gain (dimension == getDOF())

template<class T>
inline void setPGains(const T &pgain)

set P gain.

Parameters

pgain[in] position gain (dimension == getDOF())

template<class T>
inline void setDGains(const T &dgain)

set D gains.

Parameters

dgain[in] velocity gain (dimension == getDOF())

inline void setJointDamping(const Eigen::VectorXd &dampingCoefficient)

passive elements at the joints. They can be specified in the URDF file as well. Check Object/ArticulatedSystem/URDF convention in the manual

Parameters

dampingCoefficient[in] the damping coefficient vector, acting at each degrees of freedom

inline void setJointDamping(const raisim::VecDyn &dampingCoefficient)

passive elements at the joints. They can be specified in the URDF file as well. Check Object/ArticulatedSystem/URDF convention in the manual

Parameters

dampingCoefficient[in] the damping coefficient vector, acting at each degrees of freedom

void computeSparseInverse(const MatDyn &M, MatDyn &Minv) noexcept

This computes the inverse mass matrix given the mass matrix. The return type is dense. It exploits the sparsity of the mass matrix to efficiently perform the computation. The outcome also contains effects of the joint damping and strings

Parameters
  • M[in] mass matrix

  • Minv[out] inverse mass matrix

inline void massMatrixVecMul(const VecDyn &vec1, VecDyn &vec) const

this method exploits the sparsity of the mass matrix. If the mass matrix is nearly dense, it will be slower than your ordinary matrix multiplication which is probably vectorized vec = M * vec1

Parameters
  • vec[in] input vector

  • vec1[out] output vector

void ignoreCollisionBetween(size_t bodyIdx1, size_t bodyIdx2)

The bodies specified here will not collide

Parameters
  • bodyIdx1[in] first body index

  • bodyIdx2[in] second body index

inline ArticulatedSystemOption getOptions() const

Currently only supports “DO_NOT_COLLIDE_WITH_PARENT”

Returns

articulated system option

inline const std::vector<std::string> &getBodyNames() const
Returns

a vector of body names (following the joint order)

inline std::vector<VisObject> &getVisOb()
Returns

a vector of visualized bodies

inline std::vector<VisObject> &getVisColOb()
Returns

a vector of visualized collision bodies

inline void getVisObPose(size_t visObjIdx, Mat<3, 3> &rot, Vec<3> &pos) const
Parameters
  • visObjIdx[in] visual object index. Following the order specified by the vector getVisOb()

  • rot[out] orientation

  • pos[out] position

inline void getVisColObPose(size_t visColObjIdx, Mat<3, 3> &rot, Vec<3> &pos) const
Parameters
  • visColObjIdx[in] visual collision object index. Following the order specified by the vector getVisColOb()

  • rot[out] orientation

  • pos[out] position

inline const std::string &getResourceDir() const
Returns

the resource directory (for mesh files, textures, etc)

inline const std::string &getRobotDescriptionfFileName() const
Returns

the resource directory (for mesh files, textures, etc)

inline const std::string &getRobotDescriptionfTopDirName() const
Returns

the name of the URDF file (returns empty string if the robot was not specified by a URDF file)

inline const std::string &getRobotDescriptionFullPath() const
Returns

the full path to the URDF file (returns empty string if the robot was not specified by a URDF file)

inline const std::string &getRobotDescription() const
Returns

if the object was instantiated with raw URDF string, it returns the string

inline void exportRobotDescriptionToURDF(const std::string &filePath) const

if the object was instantiated with raw URDF string, it exports the robot description to an URDF file

Parameters

filePath[in] Path where the file is generated

inline void setBasePos_e(const Eigen::Vector3d &pos)

set the base position using an eigen vector

Parameters

pos[in] position of the base

inline void setBaseOrientation_e(const Eigen::Matrix3d &rot)

set the base orientation using an eigen vector

Parameters

rot[in] orientation of the base

void setBasePos(const Vec<3> &pos)

set the base position using an eigen vector

Parameters

pos[in] position of the base

void setBaseOrientation(const Mat<3, 3> &rot)

set the base orientation using an eigen vector

Parameters

rot[in] orientation of the base

inline void setActuationLimits(const Eigen::VectorXd &upper, const Eigen::VectorXd &lower)

set limits in actuation force. It can be also specified in the URDF file

Parameters
  • upper[in] upper joint force/torque limit

  • lower[in] lower joint force/torque limit

inline const VecDyn &getActuationUpperLimits() const
Returns

the upper joint torque/force limit

inline const VecDyn &getActuationLowerLimits() const
Returns

the lower joint torque/force limit

void setCollisionObjectShapeParameters(size_t id, const std::vector<double> &params)

change collision geom parameters.

Parameters
  • id[in] collision object id

  • params[in] collision object parameters (depending on the object). For a sphere, {raidus}. For a cylinder and a capsule, {radius, length} For a box, {x-dim, y-dim, z-dim}

void setCollisionObjectPositionOffset(size_t id, const Vec<3> &posOffset)

change collision geom offset from the joint position.

Parameters
  • id[in] collision object id

  • posOffset[in] the position vector expressed in the joint frame

void setCollisionObjectOrientationOffset(size_t id, const Mat<3, 3> &oriOffset)

change collision geom orientation offset from the joint frame.

Parameters
  • id[in] collision object id

  • oriOffset[in] the orientation relative to the joint frame

inline void setRotorInertia(const VecDyn &rotorInertia)

rotor inertia is a term added to the diagonal of the mass matrix. This approximates the rotor inertia. Note that this is not exactly equivalent in dynamics (due to gyroscopic effect). but it is a commonly used approximation. It can also be expressed in the URDF file

Parameters

rotorInertia[in] the rotor inertia

inline const VecDyn &getRotorInertia() const

rotor inertia is a term added to the diagonal of the mass matrix. This approximates the rotor inertia. Note that this is not exactly equivalent in dynamics (due to gyroscopic effect). but it is a commonly used approximation. It can also be expressed in the URDF file

Returns

the rotor inertia

inline Joint::Type getJointType(size_t jointIndex)

This joint indices are in the same order as the elements of the generalized velocity However, some joints have multiple degrees of freedom and they are not equal

Parameters

jointIndex[in] the joint index

Returns

the joint type

inline size_t getNumberOfJoints() const
Returns

the number of joints (same as the number of bodies)

inline JointRef getJoint(const std::string &name)

returns reference object of the joint

Parameters

name[in] joint name

Returns

a JointRef to the joint. Check the example JointRefAndLinkRef

inline LinkRef getLink(const std::string &name)

returns reference object of the joint

Parameters

name[in] the link name

Returns

a LinkRef to the link. Check the example JointRefAndLinkRef

inline const std::vector<size_t> &getMappingFromBodyIndexToGeneralizedVelocityIndex() const
Returns

a mapping that converts body index to gv index

inline const std::vector<size_t> &getMappingFromBodyIndexToGeneralizedCoordinateIndex() const
Returns

a mapping that converts body index to gv index

inline virtual ObjectType getObjectType() const final
Returns

the object type (ARTICULATED_SYSTEM)

virtual BodyType getBodyType(size_t bodyIdx) const final
Returns

the body type (STATIC, KINEMATIC, or DYNAMIC) of the specified body. It is always DYNAMIC except for the fixed base

inline virtual BodyType getBodyType() const final
Returns

the body type (STATIC, KINEMATIC, or DYNAMIC). It is always dynamic

inline void setIntegrationScheme(IntegrationScheme scheme)
Parameters

scheme[in] the integration scheme. Can be either TRAPEZOID, SEMI_IMPLICIT, EULER, or RUNGE_KUTTA_4. We recommend TRAPEZOID for systems with many collisions. RUNGE_KUTTA_4 is useful for systems with few contacts and when the integration accuracy is important

inline std::vector<contact::Single3DContactProblem const*> getJointLimitViolations(const contact::ContactProblems &problemListFromWorld)

usage example: For 1d joints (e.g., revolute or prismatic), you can get the impulse due to the joint limit as robot.getJointLimitViolations()[0]->imp_i[0] For a ball joint, all three components of imp_i represent the torque in the 3d space. The following joint returns the joint/body Id robot.getJointLimitViolations()[0]->jointId.

Returns

get contact problems associated with violated joint limits

inline void setJointLimits(const std::vector<raisim::Vec<2>> &jointLimits)

set new joint limits For revolute and prisimatic joints, the joint limit is {lower, upper} For spherical joint, the joint limit is {angle, NOT_USED}

Parameters

jointLimits[in] joint limits

inline const std::vector<raisim::Vec<2>> &getJointLimits()

get the joint limits For revolute and prisimatic joints, the joint limit is {lower, upper} For spherical joint, the joint limit is {angle, NOT_USED}

Returns

jointLimits joint limits

inline virtual void clearExternalForcesAndTorques()

Clears all external forces and torques

inline void addSpring(const SpringElement &spring)
Parameters

spring[in] Additional spring elements for joints

inline std::vector<SpringElement> &getSprings()
Returns

springs Existing spring elements on joints

void articulatedBodyAlgorithm(const Vec<3> &gravity, double dt)

to be removed. just for testing purposes

Public Static Functions

static inline void convertSparseJacobianToDense(const SparseJacobian &sparseJaco, Eigen::MatrixXd &denseJaco)
Parameters
  • sparseJaco[in] sparse Jacobian (either positional or rotational)

  • denseJaco[out] the corresponding dense Jacobian

class JointRef
class LinkRef
struct SpringElement

Public Members

size_t childBodyId = 0

the spring connects this body and its parent

double stiffness = 0

spring stiffness

Vec<4> q_ref

mounting angles for torsional and linear springs