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This paper presents design and control innovations of wearable robots that tackle two barriers to widespread adoption of powered exoskeletons, namely restriction of human movement and versatile control of wearable co-robot systems. First, the proposed quasi-direct drive actuation comprising of our customized high-torque density motors and low ratio transmission mechanism significantly reduces the mass of the robot and produces high backdrivability. Second, we derive a biomechanics model-based control that generates biological torque profile for versatile control of both squat and stoop lifting assistance. The control algorithm detects lifting postures using compact inertial measurement unit (IMU) sensors to generate an assistive profile that is proportional to the biological torque produced from our model. Experimental results demonstrate that the robot exhibits low mechanical impedance (1.5 Nm resistive torque) when it is unpowered and 0.5 Nm resistive torque with zero-torque tracking control. Root mean square (RMS) error of torque tracking is less than 0.29 Nm (1.21% error of 24 Nm peak torque). Compared with squatting without the exoskeleton, the controller reduces 87.5%, 80% and 75% of the of three knee extensor muscles (average peak EMG of 3 healthy subjects) during squat with 50% of biological torque assistance.