How RRA Works
The topics covered in this section include:
Overview
Residual reduction is a form of forward dynamics simulation that uses a tracking controller to follow model kinematics determined from the inverse kinematics. Computed muscle control (CMC) serves as the controller, but without muscles the skeleton of the model can be used to determine a mass distribution and joint kinematics that are more consistent with ground reaction forces.
Residual reduction is primarily intended for gait, i.e., movements like walking and running where the model is displaced relative to the ground while subject to ground reaction forces and torques. In this chapter, we describe an example gait model (gait2354_simbody.osim) consisting of ten rigid segments (bones) where 17 of the 23 generalized coordinates (degrees of freedom) of the model represent angles for the joints connecting the rigid segments together. Each of these 17 degrees of freedom is actuated by a single torque actuator.
The remaining 6 generalized coordinates represent the 6 degrees of freedom (3 translational, 3 rotational) between the model's pelvis and the ground. To simulate walking, we need some way of representing how the model propels itself forward relative to the ground. One way would be to use a foot-ground contact mechanism.
Instead, we present a simpler solution: represent the 6 degrees of freedom between the pelvis and the ground as a 6-degree-of-freedom joint between the pelvis and the ground, and actuate each degree of freedom with its own torque actuator. Each of these 6 actuators is called a residual actuator. Now our model has 23 degrees of freedom and 23 actuators, i.e., exactly one actuator per degree of freedom. The three residuals that actuate the 3 translational degrees of freedom between the pelvis and the ground are the residual forces, whose values we denote by ,
, and
. The 3 rotational degrees of freedom are actuated by the residual torques (or moments), whose values we denote by
,
, and
.
is the force applied along the X (forward) axis,
is the force applied along the Y (vertical) axis,
is the torque applied about the X (forward axis), and so on.
Typically, modeling assumptions (e.g., having a model with no arms), noise, and other errors from motion capture data lead to dynamic inconsistency; essentially, the ground reaction forces and acceleration estimated from measured marker kinematics for a subject do not satisfy Newton's Second Law,
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Roughly speaking, the 6 residuals amount to adding a new force to the equation that accounts for inconsistency:
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