# Articulated Systems¶ ANYmal robots (B and C versions) simulated in RaiSim.

## TL;DR¶

Click the image for vector graphics ## 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">
<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().

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 footFrameIndex = world.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 getEnergy(). 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.

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.

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

getLinkCOM method returns (a non-const reference to) a std::vector of the COM of the links. The elements are ordered by the body indicies.

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

const raisim::VecDyn &getGeneralizedCoordinate()

Return

generalized coordinate of the system

const raisim::VecDyn &getGeneralizedVelocity()

Return

generalized velocity of the system

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

Parameters
• [out] quaternion: orientation of base

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

Parameters
• [out] rotataionMatrix: orientation of base

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

Return

orientation of base

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

Parameters
• [out] position: position of base

raisim::Vec<3> getBasePosition()

Return

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.

void setGeneralizedCoordinate(const Eigen::VectorXd &jointState)

set gc of each joint in order

Parameters
• [in] jointState: generalized coordinate

void setGeneralizedCoordinate(const raisim::VecDyn &jointState)

set gc of each joint in order

Parameters
• [in] jointState: generalized coordinate

void setGeneralizedVelocity(const Eigen::VectorXd &jointVel)

set the generalized velocity

Parameters
• [in] jointVel: the generalized velocity

void setGeneralizedVelocity(const raisim::VecDyn &jointVel)

set the generalized velocity

Parameters
• [in] jointVel: the generalized velocity

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

set the generalized coordinsate of each joint in order.

Parameters
• [in] jointState: the generalized coordinate

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

set the generalized velocity of each joint in order

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

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

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

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

get both the generalized coordinate and the generalized velocity

Parameters
• [out] genco: the generalized coordinate

• [out] genvel: the generalized velocity

void getState(VecDyn &genco, VecDyn &genvel)

get both the generalized coordinate and the generalized velocity

Parameters
• [out] genco: the generalized coordinate

• [out] genvel: the generalized velocity

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
• [in] genco: the generalized coordinate

• [in] genvel: the generalized velocity

const VecDyn &getGeneralizedForce() const

Generalized force is the sum of (the feedforward force) and (the PD controller force after thresholding by the “effort” specified in the urdf)

Return

the generalized force

const VecDyn &getFeedForwardGeneralizedForce() const

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

Return

the feedforward generalized force

const MatDyn &getMassMatrix() const

get the mass matrix

Return

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

const VecDyn &getNonlinearities() const

get the coriolis and the gravitational term

Return

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

const MatDyn &getInverseMassMatrix() const

get the inverse mass matrix. Note that this is actually damped inverse. It contains the effect of damping and the spring effects

Return

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

const Vec<3> &getCompositeCOM() const

get the center of mass of the whole system

Return

the center of mass

const Mat<3, 3> &getCompositeInertia() const

get the current composite inertia of the whole system. This value assumes all joints are fixed

Return

the inertia of the coposite system

const Vec<3> &getLinearMomentum()

linear momentum of the whole system

Return

momentum

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.

Return

the generalized momentum

double getEnergy(const Vec<3> &gravity)

Return

the sum of potential/kinetic energy given the gravitational acceleration

Parameters
• [in] gravity: gravitational acceleration

double getKineticEnergy()

Return

the kinetic energy.

double getPotentialEnergy(const Vec<3> &gravity)

Return

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

Parameters
• [in] gravity: gravitational acceleration

void getAngularMomentum(const Vec<3> &referencePoint, Vec<3> &angularMomentum)

Parameters
• [in] referencePoint: the reference point about which the angular momentum is computed

• [in] angularMomentum: angular momentum about the reference point

void printOutBodyNamesInOrder() const

bodies here means moving bodies. Fixed bodies are optimized out

void printOutFrameNamesInOrder() const

frames are attached to every joint coordinate

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

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

Return

movable joint names in the joint order.

void getPosition(size_t bodyIdx, const Vec<3> &point_B, Vec<3> &point_W) const final

Return

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

Parameters
• [in] bodyIdx: The body which contains the point, can be retrieved by getBodyIdx()

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

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

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

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

Return

the coordinate frame of the given name

Parameters
• [in] nm: name of the frame

CoordinateFrame &getFrameByIdx(size_t idx)

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

Return

the coordinate frame of the given index

Parameters
• [in] idx: index of the frame

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

Return

the index of the coordinate frame of the given index.

Parameters
• [in] nm: name of the frame

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

Return

a vector of the coordinate frames

void getFramePosition(size_t frameId, Vec<3> &point_W) const

Parameters
• [in] frameId: the frame id which can be obtained by getFrameIdxByName()

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

void getFrameOrientation(size_t frameId, Mat<3, 3> &orientation_W) const

Parameters
• [in] frameId: the frame id which can be obtained by getFrameIdxByName()

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

void getFrameVelocity(size_t frameId, Vec<3> &vel_W) const

Parameters
• [in] frameId: the frame id which can be obtained by getFrameIdxByName()

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

void getFrameAngularVelocity(size_t frameId, Vec<3> &angVel_W) const

Parameters
• [in] frameId: the frame id which can be obtained by getFrameIdxByName()

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

void getFramePosition(const std::string &frameName, Vec<3> &point_W) const

Parameters
• [in] frameName: the frame name (defined in the urdf)

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

void getFrameOrientation(const std::string &frameName, Mat<3, 3> &orientation_W) const

Parameters
• [in] frameName: the frame name (defined in the urdf)

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

void getFrameVelocity(const std::string &frameName, Vec<3> &vel_W) const

Parameters
• [in] frameName: the frame name (defined in the urdf)

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

void getFrameAngularVelocity(const std::string &frameName, Vec<3> &angVel_W) const

Parameters
• [in] frameName: the frame name (defined in the urdf)

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

void getFramePosition(const CoordinateFrame &frame, Vec<3> &point_W) const

Parameters
• [in] frame: custom frame defined by the user

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

void getFrameOrientation(const CoordinateFrame &frame, Mat<3, 3> &orientation_W) const

Parameters
• [in] frame: custom frame defined by the user

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

void getFrameVelocity(const CoordinateFrame &frame, Vec<3> &vel_W) const

Parameters
• [in] frame: custom frame defined by the user

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

void getFrameAngularVelocity(const CoordinateFrame &frame, Vec<3> &angVel_W) const

Parameters
• [in] frame: custom frame defined by the user

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

void getPosition(size_t bodyIdx, Vec<3> &pos_w) const final

Parameters
• [in] bodyIdx: 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()

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

void getOrientation(size_t bodyIdx, Mat<3, 3> &rot) const final

Parameters
• [in] bodyIdx: 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()

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

void getVelocity(size_t bodyIdx, Vec<3> &vel_w) const final

Parameters
• [in] bodyIdx: 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()

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

void getAngularVelocity(size_t bodyIdx, Vec<3> &angVel_w) const

Parameters
• [in] bodyIdx: 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()

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

void getSparseJacobian(size_t bodyIdx, const Vec<3> &point_W, SparseJacobian &jaco)

Parameters
• [in] bodyIdx: 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()

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

• [out] jaco: 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)

Parameters
• [in] bodyIdx: 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()

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

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

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

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

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

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

• [out] jaco: the dense positional Jacobian

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

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

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

• [out] jaco: the dense rotational Jacobian

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

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

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

• [out] jaco: the dense positional Jacobian

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

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

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

• [out] jaco: the dense positional Jacobian

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

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

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

• [out] jaco: the dense rotational Jacobian

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

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

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

• [out] jaco: the dense rotational Jacobian

void getVelocity(const SparseJacobian &jaco, Vec<3> &pointVel) const

Parameters
• [in] jaco: the Jacobian associated with the point of interest

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

void getVelocity(size_t bodyIdx, const Vec<3> &posInBodyFrame, Vec<3> &pointVel) const

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

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

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

void getAngularVelocity(size_t bodyIdx, Vec<3> &angVel)

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

• [out] angVel: the angular velocity of the point expressed in the world frame

size_t getBodyIdx(const std::string &nm)

returns the index of the body

Return

the index of the body

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

size_t getDOF() const

Return

the degrees of freedom

size_t getGeneralizedVelocityDim() const

Return

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

size_t getGeneralizedCoordinateDim() const

Return

the dimension of generalized coordinate

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

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

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

• [out] orientation: the orientation of the body

• [out] position: the position of the body

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

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

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

• [out] position: the position of the body

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

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

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

• [out] orientation: the orientation of the body

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

Return

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

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

Return

a non-const reference to joint orientation relative to its parent, expressed in the parent frame.

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

Return

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

std::vector<double> &getMass()

You MUST call updateMassInfo() after you change the mass

Return

a non-const reference to mass of each joint.

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

Return

a non-const reference to inertia of each body.

std::vector<raisim::Vec<3>> &getLinkCOM()

Return

a non-const reference to the position of the center of the mass in the body frame.

raisim::CollisionSet &getCollisionBodies()

Return

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

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

Return

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

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”

void updateMassInfo()

This method updates the precomputed composite mass. Call this method after you change link mass

double getMass(size_t bodyIdx) const final

Return

mass of the body

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

void setMass(size_t bodyIdx, double value)

set body mass. It is indexed for each body, no each link

double getTotalMass()

Return

the total mass of the system

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

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

• [in] force: 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

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

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

• [in] force: the applied force

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

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

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

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

• [in] force: the applied force

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

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

Parameters
• [in] frame: 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.

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

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

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

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

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

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

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

• [out] vel: the contact point velocity

void setControlMode(ControlMode::Type mode)

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

ControlMode::Type getControlMode()

Return

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

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

set PD targets.

Parameters
• [in] posTarget: position target

• [in] velTarget: velocity target

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

set PD targets.

Parameters

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

set P targets.

Parameters

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

set D targets.

Parameters
• [in] velTarget: velocity target (dimension == getDOF())

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

set PD gains.

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

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

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

set PD gains.

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

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

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

set P gain.

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

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

set D gains.

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

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

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

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

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
• [in] M: mass matrix

• [out] Minv: inverse mass matrix

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
• [in] vec: input vector

• [out] vec1: output vector

void ignoreCollisionBetween(size_t bodyIdx1, size_t bodyIdx2)

The bodies specified here will not collide

Parameters
• [in] bodyIdx1: first body index

• [in] bodyIdx2: second body index

ArticulatedSystemOption getOptions()

Currently only supports “DO_NOT_COLLIDE_WITH_PARENT”

Return

articulated system option

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

Return

a vector of body names (following the joint order)

std::vector<VisObject> &getVisOb()

Return

a vector of visualized bodies

std::vector<VisObject> &getVisColOb()

Return

a vector of visualized collision bodies

void getVisObPose(size_t visObjIdx, Mat<3, 3> &rot, Vec<3> &pos)

Parameters
• [in] visObjIdx: visual object index. Following the order specified by the vector getVisOb()

• [out] rot: orientation

• [out] pos: position

void getVisColObPose(size_t visColObjIdx, Mat<3, 3> &rot, Vec<3> &pos)

Parameters
• [in] visColObjIdx: visual collision object index. Following the order specified by the vector getVisColOb()

• [out] rot: orientation

• [out] pos: position

const std::string &getResourceDir()

Return

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

const std::string &getRobotDescriptionfFileName()

Return

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

const std::string &getRobotDescriptionfTopDirName()

Return

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

const std::string &getRobotDescriptionFullPath()

Return

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

const std::string &getRobotDescription()

Return

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

void exportRobotDescriptionToURDF(const std::string &filePath)

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

Parameters
• [in] filePath: Path where the file is generated

void setBasePos_e(const Eigen::Vector3d &pos)

set the base position using an eigen vector

Parameters
• [in] pos: position of the base

void setBaseOrientation_e(const Eigen::Matrix3d &rot)

set the base orientation using an eigen vector

Parameters
• [in] rot: orientation of the base

void setBasePos(const Vec<3> &pos)

set the base position using an eigen vector

Parameters
• [in] pos: position of the base

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

set the base orientation using an eigen vector

Parameters
• [in] rot: orientation of the base

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

• [in] lower: lower joint force/torque limit

const VecDyn &getActuationUpperLimits()

Return

the upper joint torque/force limit

const VecDyn &getActuationLowerLimits()

Return

the lower joint torque/force limit

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

change collision geom parameters.

Parameters
• [in] id: collision object id

• [in] params: 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
• [in] id: collision object id

• [in] posOffset: 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
• [in] id: collision object id

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

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
• [in] rotorInertia: the rotor inertia

const VecDyn &getRotorInertia()

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

Return

the rotor inertia

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

Return

the joint type

Parameters
• [in] jointIndex: the joint index

size_t getNumberOfJoints() const

Return

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

JointRef getJoint(const std::string &name)

returns reference object of the joint

Return

a JointRef to the joint. Check the example JointRefAndLinkRef

Parameters
• [in] name: joint name

LinkRef getLink(const std::string &name)

returns reference object of the joint

Return

Parameters
• [in] name: the link name

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

Return

a mapping that converts body index to gv index

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

Return

a mapping that converts body index to gv index

ObjectType getObjectType() const final

Return

the object type (ARTICULATED_SYSTEM)

BodyType getBodyType(size_t bodyIdx) const final

Return

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

BodyType getBodyType() const final

Return

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

void setIntegrationScheme(IntegrationScheme scheme)

Parameters
• [in] scheme: 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

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

usage example: For 1d joints (e.g., revolute or prismatic), you can get the impulse due to the joint limit as robot.getJointLimitViolations()->imp_i 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()->jointId.

Return

get contact problems associated with violated joint limits

Public Static Functions

void convertSparseJacobianToDense(const SparseJacobian &sparseJaco, Eigen::MatrixXd &denseJaco)

Parameters
• [in] sparseJaco: sparse Jacobian (either positional or rotational)

• [out] denseJaco: 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