CasADi interface

CasADi interface#

This module provides an interface to CasADi, a symbolic framework for automatic differentiation and optimization.

class adam.casadi.computations.KinDynComputations(urdfstring: str, joints_name_list: list = None, root_link: str = None, gravity: array = array([0., 0., -9.80665, 0., 0., 0.]), f_opts: dict = {'cse': True, 'jit': False, 'jit_options': {'flags': '-Ofast'}})[source]#

Bases: object

Class that retrieves robot quantities using CasADi for Floating Base systems.

set_frame_velocity_representation(representation: Representations) → None[source]#

Sets the representation of the velocity of the frames

Parameters:

representation (Representations) – The representation of the velocity

mass_matrix_fun() → Function[source]#

Returns the Mass Matrix functions computed the CRBA

Returns:

Mass Matrix

Return type:

M (casADi function)

centroidal_momentum_matrix_fun() → Function[source]#

Returns the Centroidal Momentum Matrix functions computed the CRBA

Returns:

Centroidal Momentum matrix

Return type:

Jcc (casADi function)

forward_kinematics_fun(frame: str) → Function[source]#

Computes the forward kinematics relative to the specified frame

Parameters:

frame (str) – The frame to which the fk will be computed

Returns:

The fk represented as Homogenous transformation matrix

Return type:

H (casADi function)

jacobian_fun(frame: str) → Function[source]#

Returns the Jacobian relative to the specified frame

Parameters:

frame (str) – The frame to which the jacobian will be computed

Returns:

The Jacobian relative to the frame

Return type:

J_tot (casADi function)

relative_jacobian_fun(frame: str) → Function[source]#

Returns the Jacobian between the root link and a specified frame frames

Parameters:

frame (str) – The tip of the chain

Returns:

The Jacobian between the root and the frame

Return type:

J (casADi function)

jacobian_dot_fun(frame: str) → Function[source]#

Returns the Jacobian derivative relative to the specified frame

Parameters:

frame (str) – The frame to which the jacobian will be computed

Returns:

The Jacobian derivative relative to the frame

Return type:

J_dot (casADi function)

CoM_position_fun() → Function[source]#

Returns the CoM position

Returns:

The CoM position

Return type:

CoM (casADi function)

CoM_jacobian_fun() → Function[source]#

Returns the CoM Jacobian

Returns:

The CoM Jacobian

Return type:

J_com (casADi function)

bias_force_fun() → Function[source]#

Returns the bias force of the floating-base dynamics equation, using a reduced RNEA (no acceleration and external forces)

Returns:

the bias force

Return type:

h (casADi function)

coriolis_term_fun() → Function[source]#

Returns the coriolis term of the floating-base dynamics equation, using a reduced RNEA (no acceleration and external forces)

Returns:

the Coriolis term

Return type:

C (casADi function)

gravity_term_fun() → Function[source]#

Returns the gravity term of the floating-base dynamics equation, using a reduced RNEA (no acceleration and external forces)

Returns:

the gravity term

Return type:

G (casADi function)

get_total_mass() → float[source]#

Returns the total mass of the robot

Returns:

The total mass

Return type:

mass

mass_matrix(base_transform: SX, joint_positions: SX)[source]#

Returns the Mass Matrix functions computed the CRBA

Parameters:

  • base_transform (cs.SX) – The homogenous transform from base to world frame

  • joint_positions (cs.SX) – The joints position

Returns:

Mass Matrix

Return type:

M (cs.SX)

centroidal_momentum_matrix(base_transform: SX, joint_positions: SX)[source]#

Returns the Centroidal Momentum Matrix functions computed the CRBA

Parameters:

  • base_transform (cs.SX) – The homogenous transform from base to world frame

  • joint_positions (cs.SX) – The joints position

Returns:

Centroidal Momentum matrix

Return type:

Jcc (cs.SX)

relative_jacobian(frame: str, joint_positions: SX)[source]#

Returns the Jacobian between the root link and a specified frame frames

Parameters:

  • frame (str) – The tip of the chain

  • joint_positions (cs.SX) – The joints position

Returns:

The Jacobian between the root and the frame

Return type:

J (cs.SX)

jacobian_dot(frame: str, base_transform: SX, joint_positions: SX, base_velocity: SX, joint_velocities: SX) → SX[source]#

Returns the Jacobian derivative relative to the specified frame

Parameters:

  • frame (str) – The frame to which the jacobian will be computed

  • base_transform (cs.SX) – The homogenous transform from base to world frame

  • joint_positions (cs.SX) – The joints position

  • base_velocity (cs.SX) – The base velocity

  • joint_velocities (cs.SX) – The joint velocities

Returns:

The Jacobian derivative relative to the frame

Return type:

Jdot (cs.SX)

forward_kinematics(frame: str, base_transform: SX, joint_positions: SX)[source]#

Computes the forward kinematics relative to the specified frame

Parameters:

  • frame (str) – The frame to which the fk will be computed

  • base_transform (cs.SX) – The homogenous transform from base to world frame

  • joint_positions (cs.SX) – The joints position

Returns:

The fk represented as Homogenous transformation matrix

Return type:

H (cs.SX)

jacobian(frame: str, base_transform, joint_positions)[source]#

Returns the Jacobian relative to the specified frame

Parameters:

  • base_transform (cs.SX) – The homogenous transform from base to world frame

  • s (cs.SX) – The joints position

  • frame (str) – The frame to which the jacobian will be computed

Returns:

The Jacobian relative to the frame

Return type:

J_tot (cs.SX)

bias_force(base_transform: SX, joint_positions: SX, base_velocity: SX, joint_velocities: SX) → SX[source]#

Returns the bias force of the floating-base dynamics equation, using a reduced RNEA (no acceleration and external forces)

Parameters:

  • base_transform (cs.SX) – The homogenous transform from base to world frame

  • joint_positions (cs.SX) – The joints position

  • base_velocity (cs.SX) – The base velocity

  • joint_velocities (cs.SX) – The joints velocity

Returns:

the bias force

Return type:

h (cs.SX)

coriolis_term(base_transform: SX, joint_positions: SX, base_velocity: SX, joint_velocities: SX) → SX[source]#

Returns the coriolis term of the floating-base dynamics equation, using a reduced RNEA (no acceleration and external forces)

Parameters:

  • base_transform (cs.SX) – The homogenous transform from base to world frame

  • joint_positions (cs.SX) – The joints position

  • base_velocity (cs.SX) – The base velocity

  • joint_velocities (cs.SX) – The joints velocity

Returns:

the Coriolis term

Return type:

C (cs.SX)

gravity_term(base_transform: SX, joint_positions: SX) → SX[source]#

Returns the gravity term of the floating-base dynamics equation, using a reduced RNEA (no acceleration and external forces)

Parameters:

  • base_transform (cs.SX) – The homogenous transform from base to world frame

  • joint_positions (cs.SX) – The joints position

Returns:

the gravity term

Return type:

G (cs.SX)

CoM_position(base_transform: SX, joint_positions: SX) → SX[source]#

Returns the CoM position

Parameters:

  • base_transform (cs.SX) – The homogenous transform from base to world frame

  • joint_positions (cs.SX) – The joints position

Returns:

The CoM position

Return type:

CoM (cs.SX)

CoM_jacobian(base_transform: SX, joint_positions: SX) → SX[source]#

Returns the CoM Jacobian

Parameters:

  • base_transform (cs.SX) – The homogenous transform from base to world frame

  • joint_positions (cs.SX) – The joints position

Returns:

The CoM Jacobian

Return type:

J_com (cs.SX)

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