Parkinson's disease (PD) affects over 10 million worldwide, causing unstable gait and falls in 70% of patients despite medication. This leads to confidence loss, isolation, fractures, and hospitalizations. Treadmill training, augmented by mechanical/virtual-reality triggers, has proven effective in enhancing gait and reducing falls. However, underlying treadmill training mechanisms are unclear. To personalize training, we'll explore how PD patients benefit and transfer effects to daily life. This trial is part of three parallel randomized controlled trials within the Steps Against the Burden of Parkinson's Disease (CT-IDs: 6ef2e427b002, 6ef2e427b003, 6ef2e427b004) project, which will perform a pooled analysis across all sites in addition to individual RCT analyses. Each trial adheres to a shared core protocol while allowing for adaptations in the perturbation protocol, ensuring that data can be combined. Importantly, mechanistic findings and outcomes from this specific RCT will be reported independently, but also as part of a pooled analysis. In this trials, PD patients will undergo treadmill training with and without adaptations (perturbations). 12 sessions of treadmill training will be provided, with pre/post assessments and a Follow-up 12±2 weeks following T1 with pre/post assessments and a Follow-up 12±2 weeks following T1 at 8 to 12 weeks after the post assessment. For post treadmill training a phone app will be offered as a home-based speed dependent walk training intervention. This intervention is an App based training for gait adaptability and allows users to set their own training time and pace. It delivers a rhythmic metronomic beat for three different walking speeds, designed to trigger movement and encourage better walking patterns. Gait improvements are expected, driven by sensorimotor integration improving balance control. Biomechanical data analysis will reveal enhanced foot placement control. Neurophysiological changes will be studied through EEG and EMG, aiming to find improved gait stability with reduced EEG beta power and increased EEG-EMG coherence. Gait improvement in the lab might not correlate with daily-life results. Gait self-efficacy could influence transfer, prompting investigation into mechanistic associations with mobility outcomes. Remote digital tools will assess week-long mobility outcomes, employing machine learning to comprehend why some improve both in lab and life, while others don't. This will uncover mechanisms translating treatment effects into real-world outcomes, aiding personalized intervention development.