An adaptive multi-dimensional compliance model reference controller was implemented in real-time on a 4 degrees of freedom (DOF) of the humanoid Bristol-Elumotion-Robotic-Torso II (BERT II) arm in Cartesian space. The robot manipulator has been controlled in such a way as to follow the compliant passive behaviour of a reference mass-spring-damper system model subject to externally sensed forces/torques in all DOF. The relevant reference model converts all measured torques into their equivalent forces at the end-effector and reacts accordingly. The suggested control scheme takes in particular account of the multi-variable aspect and the problem of body own torques when measuring external torques. The redundant DOF were used to control the robot motion in a human-like pattern via effort minimization. Associated actuator saturation issues were addressed by incorporating a novel anti-windup (AW) compensator.