Systems and methods are presented that use the rate of change of a legged robot's centroidal angular momentum ({dot over (H)}.sub.G) in order to maintain or improve the robot's balance. In one embodiment, a control system determines the current value of {dot over (H)}.sub.G, compares this value to a threshold value, and determines an instruction to send to the robot. Executing the instruction causes the robot to remain stable or become more stable. Systems and methods are also presented that use a value derived from {dot over (H)}.sub.G in order to maintain or improve the robot's balance. In one embodiment, a control system determines the location of the Zero Rate of change of Angular Momentum (ZRAM) point (A), determines the distance between A and the location of the center of pressure of the resultant ground force, compares this value to a threshold value, and determines an instruction to send to the robot.