RigidBodyDynamics : velocity_range

[RogerP]

I am trying to understand the relationship between v and q̇ using the functions that provide the Jacobians relating the two and I wonder if someone could explain the meaning of the required velocity ranges?

The docs say:

Return the range of indices into the joint velocity vector ``v`` corresponding to joint `joint`.

E.g. For the second joint in my robot I get:

julia> state.vranges[jointVector[2]]
2:2

julia> velocity_range(state, jointVector[2])
2:2

The range is a set of indices but I don’t understand how a one-dimensional joint can span more than one index at a time. The result is always a one-dimensional Jacobian J = 1.0 which seems to imply that v == q̇ for all my joints (none are planar). Use case: I am using RBD in a state-estimator and I need to compute a number of variables to compare with the corresponding measurements from sensors.

BTW: noticed in test_mechanism_algorithms.jl there was this, which looks like a typo in the arguments:

Jv_to_q̇_j = RigidBodyDynamics.velocity_to_configuration_derivative_jacobian(joint, qj)
Jq̇_to_v_j = RigidBodyDynamics.configuration_derivative_to_velocity_jacobian(joint, qj)

[tkoolen]

@RogerP

The result is always a one-dimensional Jacobian J = 1.0 which seems to imply that v == q̇ for all my joints (none are planar).

For the Prismatic and Revolute joint types, v = \dot{q}, but that’s not the case for the SinCosRevolute, Planar, QuaternionSpherical, QuaternionFloating, or SPQuatFloating joint types.

@RogerP

The range is a set of indices but I don’t understand how a one-dimensional joint can span more than one index at a time.

The planar, spherical, and floating joint types have multiple indices into the joint velocity vector associated with them. For type stability, the return type of velocity_range is always a UnitRange, even if a joint only has a single velocity variable associated with it (resulting in e.g. the 1-length velocity range 2 : 2 you were seeing).

@RogerP

BTW: noticed in test_mechanism_algorithms.jl there was this, which looks like a typo in the arguments:

No, the Jacobian for both mappings only depends on q. The mappings themselves also depend linearly on \dot{q} or v, depending on the direction. But since these dependencies are linear, \dot{q} and v are not needed as arguments for the Jacobian functions.

[RogerP]

Brilliant!! Very clear now. Many thanks for your help!!