Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Electrical Engineering

Major Professor

Wilfrido Moreno, Ph.D.

Co-Major Professor

Alfredo Weitzenfeld, Ph.D.

Committee Member

Chung Seop Jeong, Ph.D.

Committee Member

Paris Wiley, Ph.D.

Committee Member

William Quillen, Ph.D.


Falling robot, Humanoid robot, One-legged robot, Optimal control, Fuzzy logic


Running, jumping and walking are physical activities that are performed by humans in a simple and efficient way. However, these types of movements are difficult to perform by humanoid robots. Humans perform these activities without difficulty thanks to their ability to absorb the ground impact force. The absorption of the impact force is based on the human ability to vary muscles stiffness.

The principal objective of this dissertation is to study vertical jumps in order to reduce the impact force in the landing phase of the jump motion of humanoid robots. Additionally, the impact force reduction is applied to an arm-oriented movement with the objective of preserving the integrity of falling humanoid robot.

This dissertation focuses on researching vertical jump motions by designing, implementing and testing variable stiffness control strategies based on Computed-Torque Control while tracking desired trajectories calculated using the Zero Moment Point (ZMP) and the Center of Mass (CoM) conditions. Variable stiffness method is used to reduce the impact force during the landing phase. The variable stiffness approach was previously presented by Pratt et al. in [1], where they proposed that full stiffness is not always required. In this dissertation, the variable stiffness capability is implemented without the integration of any springs or dampers. All the actuators in the robot are DC Motors and the lower stiffness is achieved by the design and implementation of PID gain values in the PID controller for each motor. The current research proposes two different approaches to generate variable stiffness. The first approach is based on an optimal control theory where the linear quadratic regulator is used to calculate the gain values of the PID controller. The second approach is based on Fuzzy logic theory and it calculates the proportional gain (KP) of the PID controller. Both approaches are based on the idea of computing the PID gains to allow for the displacement of the DC motor positions with respect to the target positions during the landing phase. While a DC motor moves from the target position, the robot CoM changes towards a lower position reducing the impact force. The Fuzzy approach uses an estimation of the impact velocity and a specified desired soft landing level at the moment of impact in order to calculate the P gain of the PID controller. The optimal approach uses the mathematical model of the motor and the factor, which affects the Q matrix of the Linear Quadratic Regulator (LQR), in order to calculate the new PID values.

A One-legged robot is used to perform the jump motion verification in this research. In addition, repeatability experiments were also successfully performed with both the optimal control and the Fuzzy logic methods. The results are evaluated and compared according to the impact force reduction and the robot balance during the landing phase. The impact force calculation is based on the displacement of the CoM during the landing phase. The impact force reduction is accomplished by both methods; however, the robot balance shows a considerable improvement with the optimal control approach in comparison to the Fuzzy logic method. In addition, the Optimal Variable Stiffness method was successfully implemented and tested in Falling Robots. The robot integrity is accomplished by applying the Optimal Variable Stiffness control method to reduce the impact force on the arm joints, shoulders and elbows.

Included in

Robotics Commons