One of the last exponents of the French polyphonic music tradition established by Jean Titelouze and Louis Couperin, Roberday is best remembered today for his Fugues et caprices, a collection of four-part contrapuntal organ pieces.
After his father's death, Roberday was appointed King's goldsmith, and in 1659 he bought the job of the official manservant to the Queen.
Roberday's only extant work is Fugues et caprices, a collection of organ pieces published in 1660 in Paris.
The fugues use subjects with extensive usage of longer note values, which are modified in the caprices to better suit their fast tempi.
The collection shows considerable Italian influence and many of the pieces are based on themes from miscellaneous composers of the era, including Girolamo Frescobaldi, Louis Couperin, Jean-Henri d'Anglebert, Johann Jakob Froberger, Francesco Cavalli and others.