Gait and REM Sleep Behavior Disorder

Many people with idiopathic rapid eye movement (REM) sleep behavior disorder (RBD) have an underlying synucleinopathy, the most common of which are Parkinson's disease (PD) and Lewy body disease. Identifying additional abnormal clinical features may help in identifying those at greater risk of evolving to a more severe syndrome. Because gait disorders are common in the synucleinopathies, early abnormalities in gait in those with RBD could help in identifying those at increased risk of developing overt parkinsonism and/or cognitive impairment. The investigators aim to identify subtle gait abnormalities in idiopathic RBD and to identify sensitive and early biomarkers: 1. to detect subtle gait disorders in pre-symptomatic stage of synucleinopathy and 2. to track their evolution in the parallel with the disease progression. Main objective: In comparison with age and gender matched-controls, to identify in patients with RBD a larger reduction of gait velocity (and other abnormalities of spatio-temporal characteristics of gait) between a single (gait) and a dual-task (gait+cognitive task). Secondary objective: 1. In comparison with age and gender matched-PD patients, to identify in patients with RBD a smaller reduction of gait velocity (and other abnormalities of spatio-temporal characteristics of gait) between a single (gait) and a dual-task (gait+cognitive task). 2. In patients with RBD to identify correlations between the spatio-temporal characteristics modifications of gait between a single (gait) and a dual-task (gait+cognitive task) and the percentage of REM without atonia - the dopamine transporter (DAT) density using FP-CIT single-photon emission computed tomography; the reduction of the olfactory discrimination and thresholds. 3. In patients with RBD to track the spatio-temporal characteristics evolution of gait over time (every 6 months for 2 years)