Joint Acceleration Task

Acceleration tasks can be expressed in either joint-space or in operational-space. Here, the operational-space form is presented but the joint-space form can easily be produced as,

(1) $\fjsa_{i} = \left\| \jsrd - \jsrd_{i}^{\text{des}} \right\|_{2}^{2} \tc$

with

(2) $\Ejsa &= \bmat{I & \0 }$

(3) $\fvecjsa &= \jsrd_{i}^{\text{des}}\tc$

where $I$ is the identity matrix. Substituting (2) and (3) into (1) gives,

(4) $\fjsa_{i} = \left\| \Ejsa \optvar - \fvecjsa \right\|_{2}^{2} \tp$