Objective. A four-dimensional robust optimisation (4DRO) is usually employed when the tumour respiratory motion needs to be addressed. However, it is computationally demanding, and an automated method is preferable for adaptive planning to avoid manual trial-and-error. This study proposes a 4DRO technique based on dose mimicking for automated adaptive planning. Approach. Initial plans for 4DRO intensity modulated proton therapy were created on an average CT for four patients with clinical target volume (CTV) in the lung, oesophagus, or pancreas, respectively. These plans were robustly optimised using three phases of four-dimensional computed tomography (4DCT) and accounting for setup and density uncertainties. Weekly 4DCTs were used for adaptive replanning, using a constant relative biological effectiveness (cRBE) of 1.1. Two methods were used: (1) template-based adaptive (TA) planning and (2) dose-mimicking-based adaptive (MA) planning. The plans were evaluated using variable RBE (vRBE) weighted doses and biologically consistent dose accumulation (BCDA). Main results. MA and TA plans had comparable CTV coverage except for one patient where the MA plan had a higher D98 and lower D2 but with an increased D2 in few organs at risk (OARs). CTV D98 deviations in non-adaptive plans from the initial plans were up to −7.2 percentage points (p.p.) in individual cases and −1.8 p.p. when using BCDA. For the OARs, MA plans showed a reduced mean dose and D2 compared to the TA plans, with few exceptions. The vRBE-weighted accumulated doses had a mean dose and D2 difference of up to 0.3 Gy and 0.5 Gy, respectively, in the OARs with respect to cRBE-weighted doses. Significance. MA plans indicate better performance in target coverage and OAR dose sparing compared to the TA plans in 4DRO adaptive planning. Moreover, MA method is capable of handling both forms of anatomical variation, namely, changes in density and relative shifts in the position of OARs.