Robert started riding at age six. His father, Harvey Smith, was an equestrian rider, so he was encouraged to follow in his father's footsteps.
He was winner of the Animal Health Trust UK Equestrian Award in 2004. In 1979, at just 17, he became the youngest winner of the King George V Gold Cup at the Royal International Horse Show on Upton.
His father Harvey competed in show jumping at the 1968 and 1972 Olympic Games. He also won a bronze medal in the individual event at the 1970 World Championships. His brother Steven won a silver medal in show jumping team event at the 1984 Olympic Games in Los Angeles.
His hobbies are boxing, tennis, snooker, golf and football.