We use integral field spectroscopy, from the SWIFT and Palm3K instruments, to perform a spatially-resolved spectroscopic analysis of four nearby highly star-forming `green pea (GP) galaxies, that are likely analogues of star-forming systems at z~2.5-3. By studying emission-line maps in H$alpha$, [NII]$lambda lambda$6548,6584 and [SII]$lambda$$lambda$6716,6731, we explore the kinematic morphology of these systems and constrain properties such as gas-phase metallicities, electron densities and gas-ionization mechanisms. Two of our GPs are rotationally-supported while the others are dispersion-dominated systems. The rotationally-supported galaxies both show evidence for recent or ongoing mergers. However, given that these systems have intact disks, these interactions are likely to have low mass ratios (i.e. minor mergers), suggesting that the minor-merger process may be partly responsible for the high SFRs seen in these GPs. Nevertheless, the fact that the other two GPs appear morphologically undisturbed suggests that mergers (including minor mergers) are not necessary for driving the high star formation rates in such galaxies. We show that the GPs are metal-poor systems (25-40 per cent of solar) and that the gas ionization is not driven by AGN in any of our systems, indicating that AGN activity is not co-eval with star formation in these starbursting galaxies.