Involved in the degradation of serine via 3-hydroxypyruvate. Catalyzes the ATP-dependent phosphorylation of D-glycerate to 2-phosphoglycerate. (R)-glycerate + ATP = (2R)-2-phosphoglycerate + ADP + H(+) kcat is 14.4 sec(-1) for phosphorylation of D-glycerate. Homodimer. Belongs to the glycerate kinase type-1 family.