The movement of voluntary skeletal muscles involved in doing calisthenics is under the control of the

The somatic nervous system

Explanation:

Voluntary skeletal muscles are the muscle type which becomes activated and perform their function when they get some stimulus or they receive some signal. The signals in the body travel in the body through the neurons in the form of electrical signals.

Therefore the signals through the neurons play a major role and the type of nervous tissue which controls these voluntary actions of the muscle is known as the somatic nervous system. The somatic nervous system contains two types of neurons: the neurons which bring the signals from organ to the brain is a sensory neuron and the neuron which brings signals from the brain to muscle is the motor neuron.

Thus, the somatic nervous system is the correct answer.