Drake
Drake C++ Documentation
InverseKinematics Class Reference

## Detailed Description

Solves an inverse kinematics (IK) problem on a MultibodyPlant, to find the postures of the robot satisfying certain constraints.

The decision variables include the generalized position of the robot.

#include <drake/multibody/inverse_kinematics/inverse_kinematics.h>

## Public Member Functions

~InverseKinematics ()

InverseKinematics (const MultibodyPlant< double > &plant, bool with_joint_limits=true)
Constructs an inverse kinematics problem for a MultibodyPlant. More...

InverseKinematics (const MultibodyPlant< double > &plant, systems::Context< double > *plant_context, bool with_joint_limits=true)
Constructs an inverse kinematics problem for a MultibodyPlant. More...

solvers::Binding< solvers::ConstraintAddPositionConstraint (const Frame< double > &frameB, const Eigen::Ref< const Eigen::Vector3d > &p_BQ, const Frame< double > &frameA, const Eigen::Ref< const Eigen::Vector3d > &p_AQ_lower, const Eigen::Ref< const Eigen::Vector3d > &p_AQ_upper)
Adds the kinematic constraint that a point Q, fixed in frame B, should lie within a bounding box expressed in another frame A as p_AQ_lower <= p_AQ <= p_AQ_upper, where p_AQ is the position of point Q measured and expressed in frame A. More...

solvers::Binding< solvers::ConstraintAddPositionConstraint (const Frame< double > &frameB, const Eigen::Ref< const Eigen::Vector3d > &p_BQ, const Frame< double > &frameAbar, const std::optional< math::RigidTransformd > &X_AbarA, const Eigen::Ref< const Eigen::Vector3d > &p_AQ_lower, const Eigen::Ref< const Eigen::Vector3d > &p_AQ_upper)
Adds the kinematic constraint that a point Q, fixed in frame B, should lie within a bounding box expressed in another frame A as p_AQ_lower <= p_AQ <= p_AQ_upper, where p_AQ is the position of point Q measured and expressed in frame A. More...

solvers::Binding< solvers::CostAddPositionCost (const Frame< double > &frameA, const Eigen::Ref< const Eigen::Vector3d > &p_AP, const Frame< double > &frameB, const Eigen::Ref< const Eigen::Vector3d > &p_BQ, const Eigen::Ref< const Eigen::Matrix3d > &C)
Adds a cost of the form (p_AP - p_AQ)ᵀ C (p_AP - p_AQ), where point P is specified relative to frame A and point Q is specified relative to frame B, and the cost is evaluated in frame A. More...

solvers::Binding< solvers::ConstraintAddOrientationConstraint (const Frame< double > &frameAbar, const math::RotationMatrix< double > &R_AbarA, const Frame< double > &frameBbar, const math::RotationMatrix< double > &R_BbarB, double theta_bound)
Constrains that the angle difference θ between the orientation of frame A and the orientation of frame B to satisfy θ ≤ θ_bound. More...

solvers::Binding< solvers::CostAddOrientationCost (const Frame< double > &frameAbar, const math::RotationMatrix< double > &R_AbarA, const Frame< double > &frameBbar, const math::RotationMatrix< double > &R_BbarB, double c)
Adds a cost of the form c * (1 - cos(θ)), where θ is the angle between the orientation of frame A and the orientation of frame B, and c is a cost scaling. More...

solvers::Binding< solvers::ConstraintAddGazeTargetConstraint (const Frame< double > &frameA, const Eigen::Ref< const Eigen::Vector3d > &p_AS, const Eigen::Ref< const Eigen::Vector3d > &n_A, const Frame< double > &frameB, const Eigen::Ref< const Eigen::Vector3d > &p_BT, double cone_half_angle)
Constrains a target point T to be within a cone K. More...

solvers::Binding< solvers::ConstraintAddAngleBetweenVectorsConstraint (const Frame< double > &frameA, const Eigen::Ref< const Eigen::Vector3d > &na_A, const Frame< double > &frameB, const Eigen::Ref< const Eigen::Vector3d > &nb_B, double angle_lower, double angle_upper)
Constrains that the angle between a vector na and another vector nb is between [θ_lower, θ_upper]. More...

solvers::Binding< solvers::CostAddAngleBetweenVectorsCost (const Frame< double > &frameA, const Eigen::Ref< const Eigen::Vector3d > &na_A, const Frame< double > &frameB, const Eigen::Ref< const Eigen::Vector3d > &nb_B, double c)
Add a cost c * (1-cosθ) where θ is the angle between the vector na and nb. More...

solvers::Binding< solvers::ConstraintAddMinimumDistanceConstraint (double minimum_distance, double influence_distance_offset=1)
Adds the constraint that the pairwise distance between objects should be no smaller than minimum_distance. More...

solvers::Binding< solvers::ConstraintAddDistanceConstraint (const SortedPair< geometry::GeometryId > &geometry_pair, double distance_lower, double distance_upper)
Adds the constraint that the distance between a pair of geometries is within some bounds. More...

solvers::Binding< solvers::ConstraintAddPointToPointDistanceConstraint (const Frame< double > &frame1, const Eigen::Ref< const Eigen::Vector3d > &p_B1P1, const Frame< double > &frame2, const Eigen::Ref< const Eigen::Vector3d > &p_B2P2, double distance_lower, double distance_upper)
Add a constraint that the distance between point P1 attached to frame 1 and point P2 attached to frame 2 is within the range [distance_lower, distance_upper]. More...

solvers::Binding< solvers::ConstraintAddPolyhedronConstraint (const Frame< double > &frameF, const Frame< double > &frameG, const Eigen::Ref< const Eigen::Matrix3Xd > &p_GP, const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::VectorXd > &b)
Adds the constraint that the position of P1, ..., Pn satisfy A * [p_FP1; p_FP2; ...; p_FPn] <= b. More...

const solvers::VectorXDecisionVariableq () const
Getter for q. More...

const solvers::MathematicalProgramprog () const
Getter for the optimization program constructed by InverseKinematics. More...

solvers::MathematicalProgramget_mutable_prog () const
Getter for the optimization program constructed by InverseKinematics. More...

const systems::Context< double > & context () const
Getter for the plant context. More...

systems::Context< double > * get_mutable_context ()
Getter for the mutable plant context. More...

Does not allow copy, move, or assignment
InverseKinematics (const InverseKinematics &)=delete

InverseKinematicsoperator= (const InverseKinematics &)=delete

InverseKinematics (InverseKinematics &&)=delete

InverseKinematicsoperator= (InverseKinematics &&)=delete

## ◆ InverseKinematics() [1/4]

 InverseKinematics ( const InverseKinematics & )
delete

## ◆ InverseKinematics() [2/4]

 InverseKinematics ( InverseKinematics && )
delete

## ◆ ~InverseKinematics()

 ~InverseKinematics ( )

## ◆ InverseKinematics() [3/4]

 InverseKinematics ( const MultibodyPlant< double > & plant, bool with_joint_limits = true )
explicit

Constructs an inverse kinematics problem for a MultibodyPlant.

This constructor will create and own a context for

Parameters
 plant. plant The robot on which the inverse kinematics problem will be solved. with_joint_limits If set to true, then the constructor imposes the joint limit (obtained from plant.GetPositionLowerLimits() and plant.GetPositionUpperLimits(). If set to false, then the constructor does not impose the joint limit constraints in the constructor.
Note
The inverse kinematics problem constructed in this way doesn't permit collision related constraint (such as calling AddMinimumDistanceConstraint). To enable collision related constraint, call InverseKinematics(const MultibodyPlant<double>& plant, systems::Context<double>* plant_context);

## ◆ InverseKinematics() [4/4]

 InverseKinematics ( const MultibodyPlant< double > & plant, systems::Context< double > * plant_context, bool with_joint_limits = true )

Constructs an inverse kinematics problem for a MultibodyPlant.

If the user wants to solve the problem with collision related constraint (like calling AddMinimumDistanceConstraint), please use this constructor.

Parameters
 plant The robot on which the inverse kinematics problem will be solved. This plant should have been connected to a SceneGraph within a Diagram context The context for the plant. This context should be a part of the Diagram context. To construct a plant connected to a SceneGraph, with the corresponding plant_context, the steps are // 1. Add a diagram containing the MultibodyPlant and SceneGraph systems::DiagramBuilder builder; auto items = AddMultibodyPlantSceneGraph(&builder, 0.0); // 2. Add collision geometries to the plant Parser(&(items.plant)).AddModels("model.sdf"); // 3. Construct the diagram auto diagram = builder.Build(); // 4. Create diagram context. auto diagram_context= diagram->CreateDefaultContext(); // 5. Get the context for the plant. auto plant_context = &(diagram->GetMutableSubsystemContext(items.plant, diagram_context.get())); This context will be modified during calling ik.prog.Solve(...). When Solve() returns result, context will store the optimized posture, namely plant.GetPositions(*context) will be the same as in result.GetSolution(ik.q()). The user could then use this context to perform kinematic computation (like computing the position of the end-effector etc.). with_joint_limits If set to true, then the constructor imposes the joint limit (obtained from plant.GetPositionLowerLimits() and plant.GetPositionUpperLimits(). If set to false, then the constructor does not impose the joint limit constraints in the constructor.

## Member Function Documentation

 solvers::Binding AddAngleBetweenVectorsConstraint ( const Frame< double > & frameA, const Eigen::Ref< const Eigen::Vector3d > & na_A, const Frame< double > & frameB, const Eigen::Ref< const Eigen::Vector3d > & nb_B, double angle_lower, double angle_upper )

Constrains that the angle between a vector na and another vector nb is between [θ_lower, θ_upper].

na is fixed to a frame A, while nb is fixed to a frame B. Mathematically, if we denote na_unit_A as na expressed in frame A after normalization (na_unit_A has unit length), and nb_unit_B as nb expressed in frame B after normalization, the constraint is cos(θ_upper) ≤ na_unit_Aᵀ * R_AB * nb_unit_B ≤ cos(θ_lower), where R_AB is the rotation matrix, representing the orientation of frame B expressed in frame A.

Parameters
 frameA The frame to which na is fixed. na_A The vector na fixed to frame A, expressed in frame A.
Precondition
na_A should be a non-zero vector.
Exceptions
 std::exception if na_A is close to zero.
Parameters
 frameB The frame to which nb is fixed. nb_B The vector nb fixed to frame B, expressed in frame B.
Precondition
nb_B should be a non-zero vector.
Exceptions
 std::exception if nb_B is close to zero.
Parameters
 angle_lower The lower bound on the angle between na and nb. It is denoted as θ_lower in the documentation. angle_lower is in radians.
Precondition
angle_lower >= 0.
Exceptions
 std::exception if angle_lower is negative.
Parameters
 angle_upper The upper bound on the angle between na and nb. it is denoted as θ_upper in the class documentation. angle_upper is in radians.
Precondition
angle_lower <= angle_upper <= pi.
Exceptions
 std::exception if angle_upper is outside the bounds.

 solvers::Binding AddAngleBetweenVectorsCost ( const Frame< double > & frameA, const Eigen::Ref< const Eigen::Vector3d > & na_A, const Frame< double > & frameB, const Eigen::Ref< const Eigen::Vector3d > & nb_B, double c )

Add a cost c * (1-cosθ) where θ is the angle between the vector na and nb.

na is fixed to a frame A, while nb is fixed to a frame B.

Parameters
 frameA The frame to which na is fixed. na_A The vector na fixed to frame A, expressed in frame A.
Precondition
na_A should be a non-zero vector.
Exceptions
 std::exception if na_A is close to zero.
Parameters
 frameB The frame to which nb is fixed. nb_B The vector nb fixed to frame B, expressed in frame B.
Precondition
nb_B should be a non-zero vector.
Exceptions
 std::exception if nb_B is close to zero.
Parameters
 c The cost is c * (1-cosθ).

 solvers::Binding AddDistanceConstraint ( const SortedPair< geometry::GeometryId > & geometry_pair, double distance_lower, double distance_upper )

Adds the constraint that the distance between a pair of geometries is within some bounds.

Parameters
 geometry_pair The pair of geometries between which the distance is constrained. Notice that we only consider the distance between a static geometry and a dynamic geometry, or a pair of dynamic geometries. We don't allow constraining the distance between two static geometries. distance_lower The lower bound on the distance. distance_upper The upper bound on the distance.

 solvers::Binding AddGazeTargetConstraint ( const Frame< double > & frameA, const Eigen::Ref< const Eigen::Vector3d > & p_AS, const Eigen::Ref< const Eigen::Vector3d > & n_A, const Frame< double > & frameB, const Eigen::Ref< const Eigen::Vector3d > & p_BT, double cone_half_angle )

Constrains a target point T to be within a cone K.

The point T ("T" stands for "target") is fixed in a frame B, with position p_BT. The cone originates from a point S ("S" stands for "source"), fixed in frame A with position p_AS, with the axis of the cone being n, also fixed in frame A. The half angle of the cone is θ. A common usage of this constraint is that a camera should gaze at some target; namely the target falls within a gaze cone, originating from the camera eye.

Parameters
 frameA The frame where the gaze cone is fixed to. p_AS The position of the cone source point S, measured and expressed in frame A. n_A The directional vector representing the center ray of the cone, expressed in frame A.
Precondition
n_A cannot be a zero vector.
Exceptions
 std::exception is n_A is close to a zero vector.
Parameters
 frameB The frame where the target point T is fixed to. p_BT The position of the target point T, measured and expressed in frame B. cone_half_angle The half angle of the cone. We denote it as θ in the documentation. cone_half_angle is in radians.
Precondition
0 <= cone_half_angle <= pi.
Exceptions
 std::exception if cone_half_angle is outside of the bound.

 solvers::Binding AddMinimumDistanceConstraint ( double minimum_distance, double influence_distance_offset = 1 )

Adds the constraint that the pairwise distance between objects should be no smaller than minimum_distance.

We consider the distance between pairs of

1. Anchored (static) object and a dynamic object.
2. A dynamic object and another dynamic object, if one is not the parent link of the other.
Parameters
 minimum_distance The minimum allowed value, dₘᵢₙ, of the signed distance between any candidate pair of geometries. influence_distance_offset The difference (in meters) between the influence distance, d_influence, and the minimum distance, dₘᵢₙ. This value must be finite and strictly positive, as it is used to scale the signed distances between pairs of geometries. Smaller values may improve performance, as fewer pairs of geometries need to be considered in each constraint evaluation. Default: 1 meter
MinimumDistanceConstraint for more details on the constraint formulation.
Precondition
The MultibodyPlant passed to the constructor of this has registered its geometry with a SceneGraph.
0 < influence_distance_offset < ∞

 solvers::Binding AddOrientationConstraint ( const Frame< double > & frameAbar, const math::RotationMatrix< double > & R_AbarA, const Frame< double > & frameBbar, const math::RotationMatrix< double > & R_BbarB, double theta_bound )

Constrains that the angle difference θ between the orientation of frame A and the orientation of frame B to satisfy θ ≤ θ_bound.

Frame A is fixed to frame A_bar, with orientation R_AbarA measured in frame A_bar. Frame B is fixed to frame B_bar, with orientation R_BbarB measured in frame B_bar. The angle difference between frame A's orientation R_WA and B's orientation R_WB is θ, (θ ∈ [0, π]), if there exists a rotation axis a, such that rotating frame A by angle θ about axis a aligns it with frame B. Namely R_AB = I + sinθ â + (1-cosθ)â² (1) where R_AB is the orientation of frame B expressed in frame A. â is the skew symmetric matrix of the rotation axis a. Equation (1) is the Rodrigues formula that computes the rotation matrix from a rotation axis a and an angle θ, https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula If the users want frame A and frame B to align perfectly, they can set θ_bound = 0. Mathematically, this constraint is imposed as trace(R_AB) ≥ 2cos(θ_bound) + 1 (1) To derive (1), using Rodrigues formula R_AB = I + sinθ â + (1-cosθ)â² where trace(R_AB) = 2cos(θ) + 1 ≥ 2cos(θ_bound) + 1

Parameters
 frameAbar frame A_bar, the frame A is fixed to frame A_bar. R_AbarA The orientation of frame A measured in frame A_bar. frameBbar frame B_bar, the frame B is fixed to frame B_bar. R_BbarB The orientation of frame B measured in frame B_bar. theta_bound The bound on the angle difference between frame A's orientation and frame B's orientation. It is denoted as θ_bound in the documentation. theta_bound is in radians.

 solvers::Binding AddOrientationCost ( const Frame< double > & frameAbar, const math::RotationMatrix< double > & R_AbarA, const Frame< double > & frameBbar, const math::RotationMatrix< double > & R_BbarB, double c )

Adds a cost of the form c * (1 - cos(θ)), where θ is the angle between the orientation of frame A and the orientation of frame B, and c is a cost scaling.

Parameters
 frameAbar A frame on the MultibodyPlant. R_AbarA The rotation matrix describing the orientation of frame A relative to Abar. frameBbar A frame on the MultibodyPlant. R_BbarB The rotation matrix describing the orientation of frame B relative to Bbar. c A scalar cost weight.

 solvers::Binding AddPointToPointDistanceConstraint ( const Frame< double > & frame1, const Eigen::Ref< const Eigen::Vector3d > & p_B1P1, const Frame< double > & frame2, const Eigen::Ref< const Eigen::Vector3d > & p_B2P2, double distance_lower, double distance_upper )

Add a constraint that the distance between point P1 attached to frame 1 and point P2 attached to frame 2 is within the range [distance_lower, distance_upper].

Parameters
 frame1 The frame to which P1 is attached. p_B1P1 The position of P1 measured and expressed in frame 1. frame2 The frame to which P2 is attached. p_B2P2 The position of P2 measured and expressed in frame 2. distance_lower The lower bound on the distance. distance_upper The upper bound on the distance.

 solvers::Binding AddPolyhedronConstraint ( const Frame< double > & frameF, const Frame< double > & frameG, const Eigen::Ref< const Eigen::Matrix3Xd > & p_GP, const Eigen::Ref< const Eigen::MatrixXd > & A, const Eigen::Ref< const Eigen::VectorXd > & b )

Adds the constraint that the position of P1, ..., Pn satisfy A * [p_FP1; p_FP2; ...; p_FPn] <= b.

Parameters
 frameF The frame in which the position P is measured and expressed frameG The frame in which the point P is rigidly attached. p_GP p_GP.col(i) is the position of the i'th point Pi measured and expressed in frame G. A We impose the constraint A * [p_FP1; p_FP2; ...; p_FPn] <= b.
Precondition
A.cols() = 3 * p_GP.cols();
Parameters
 b We impose the constraint A * [p_FP1; p_FP2; ...; p_FPn] <= b

 solvers::Binding AddPositionConstraint ( const Frame< double > & frameB, const Eigen::Ref< const Eigen::Vector3d > & p_BQ, const Frame< double > & frameA, const Eigen::Ref< const Eigen::Vector3d > & p_AQ_lower, const Eigen::Ref< const Eigen::Vector3d > & p_AQ_upper )

Adds the kinematic constraint that a point Q, fixed in frame B, should lie within a bounding box expressed in another frame A as p_AQ_lower <= p_AQ <= p_AQ_upper, where p_AQ is the position of point Q measured and expressed in frame A.

Parameters
 frameB The frame in which point Q is fixed. p_BQ The position of the point Q, rigidly attached to frame B, measured and expressed in frame B. frameA The frame in which the bounding box p_AQ_lower <= p_AQ <= p_AQ_upper is expressed. p_AQ_lower The lower bound on the position of point Q, measured and expressed in frame A. p_AQ_upper The upper bound on the position of point Q, measured and expressed in frame A.

 solvers::Binding AddPositionConstraint ( const Frame< double > & frameB, const Eigen::Ref< const Eigen::Vector3d > & p_BQ, const Frame< double > & frameAbar, const std::optional< math::RigidTransformd > & X_AbarA, const Eigen::Ref< const Eigen::Vector3d > & p_AQ_lower, const Eigen::Ref< const Eigen::Vector3d > & p_AQ_upper )

Adds the kinematic constraint that a point Q, fixed in frame B, should lie within a bounding box expressed in another frame A as p_AQ_lower <= p_AQ <= p_AQ_upper, where p_AQ is the position of point Q measured and expressed in frame A.

Parameters
 frameB The frame in which point Q is fixed. p_BQ The position of the point Q, rigidly attached to frame B, measured and expressed in frame B. frameAbar We will compute frame A from frame Abar. The bounding box p_AQ_lower <= p_AQ <= p_AQ_upper is expressed in frame A. X_AbarA The relative transform between frame Abar and A. If empty, then we use the identity transform. p_AQ_lower The lower bound on the position of point Q, measured and expressed in frame A. p_AQ_upper The upper bound on the position of point Q, measured and expressed in frame A.

 solvers::Binding AddPositionCost ( const Frame< double > & frameA, const Eigen::Ref< const Eigen::Vector3d > & p_AP, const Frame< double > & frameB, const Eigen::Ref< const Eigen::Vector3d > & p_BQ, const Eigen::Ref< const Eigen::Matrix3d > & C )

Adds a cost of the form (p_AP - p_AQ)ᵀ C (p_AP - p_AQ), where point P is specified relative to frame A and point Q is specified relative to frame B, and the cost is evaluated in frame A.

Parameters
 frameA The frame in which point P's position is measured. p_AP The point P. frameB The frame in which point Q's position is measured. p_BQ The point Q. C A 3x3 matrix representing the cost in quadratic form.

## ◆ context()

 const systems::Context& context ( ) const

Getter for the plant context.

## ◆ get_mutable_context()

 systems::Context* get_mutable_context ( )

Getter for the mutable plant context.

## ◆ get_mutable_prog()

 solvers::MathematicalProgram* get_mutable_prog ( ) const

Getter for the optimization program constructed by InverseKinematics.

## ◆ operator=() [1/2]

 InverseKinematics& operator= ( InverseKinematics && )
delete

## ◆ operator=() [2/2]

 InverseKinematics& operator= ( const InverseKinematics & )
delete

## ◆ prog()

 const solvers::MathematicalProgram& prog ( ) const

Getter for the optimization program constructed by InverseKinematics.

## ◆ q()

 const solvers::VectorXDecisionVariable& q ( ) const

Getter for q.

q is the decision variable for the generalized positions of the robot.

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