  The transition helicity amplitudes from the proton ground state to the
$N(1440)1/2^+$, $N(1520)3/2^-$, and $\Delta(1620)1/2^-$ resonances
($\gamma_vpN^*$ electrocouplings) were determined from the analysis of nine
independent one-fold differential $\pi^+ \pi^- p$ electroproduction cross
sections off a proton target, taken with CLAS at photon virtualities 0.5
GeV$^2$ $< Q^2 <$ 1.5 GeV$^2$. The phenomenological reaction model employed for
separation of the resonant and non-resonant contributions to this exclusive
channel was further developed. The $N(1440)1/2^+$, $N(1520)3/2^-$, and
$\Delta(1620)1/2^-$ electrocouplings were obtained from the resonant amplitudes
of charged double-pion electroproduction off the proton in the aforementioned
area of photon virtualities for the first time. Consistent results on
$\gamma_vpN^*$ electrocouplings available from independent analyses of several
$W$-intervals with different non-resonant contributions offer clear evidence
for the reliable extraction of these fundamental quantities. These studies also
improved the knowledge on hadronic branching ratios for the $N(1440)1/2^+$,
$N(1520)3/2^-$, and $\Delta(1620)1/2^-$ decays to the $\pi \Delta$ and $\rho N$
final states. These new results provide a substantial impact on the QCD-based
approaches that describe the $N^*$ structure and demonstrate the capability to
explore fundamental ingredients of the non-perturbative strong interaction that
are behind the excited nucleon state formation.
