Table 1:
Summary of the Equations for Our Discrete and Rhythmic Model Equations.
DiscreteRhythmic
Transformation system:  Transformation system:
Equation 2.1  Equation 2.1

Canonical system:  Canonical system:
Equation 2.2  Equation 2.5
Forcing term:  Forcing term:
Equation 2.3  Equation 2.6

Optional terms:  Optional terms:
Equation 2.15  Equation 2.15
Equation 2.20

hi= equal spacing in   hi= equal spacing in

DiscreteRhythmic
Transformation system:  Transformation system:
Equation 2.1  Equation 2.1

Canonical system:  Canonical system:
Equation 2.2  Equation 2.5
Forcing term:  Forcing term:
Equation 2.3  Equation 2.6

Optional terms:  Optional terms:
Equation 2.15  Equation 2.15
Equation 2.20

hi= equal spacing in   hi= equal spacing in

Notes: The high-level design parameters of the discrete system are , the temporal scaling factor, and g, the goal position. The design parameters of the rhythmic system are g, the baseline of the oscillation; , the period divided by ; and r, the amplitude of oscillations. The terms Ct and Cc are coupling terms that are application dependent and explained in section 3.2. The parameters wi are fitted to a demonstrated trajectory using locally weighted learning. The parameters , and ci are positive constants. Unless stated otherwise, the values at the bottom of the table are used in this letter.

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