2-norm, infinity-norm continuous switching resolution in biarticularly actuated robot arms

In the resolution of redundant systems, two popular resolution schemes, optimization using 2-norm and infinity-norm, have been commonly employed. However, each finds its greatest utility in resolution in very different circumstances. The 2-norm optimizes in analog to minimizing system energy (sometimes by putting large strain on individual actuators). Likewise, the infinity-norm minimizes individual actuator contributions, at the expense of total system efficiency. As such, it would be preferable to utilize a resolution system which optimizes along the 2-norm while actuator levels are low and of little concern, and switches to infinity-norm when individual actuator levels grow too large. Although previously hypothesized, this paper marks the first successful realization of the described resolution scheme and is proposed for use in resolving biarticular actuation redundancy- a biologically inspired actuation structure enabling effective force transfer, stiffness regulation, and homogeneous force output. To realize this switching system, a resolution scheme called the Cascaded Generalized Inverse (CGI) is used to enable continuous switching between the two norms at a pre-defined switching threshold. Proof of continuity is demonstrated, and implementation is simulated.