Date of Defense
6-5-2025 11:00 AM
Location
F1, 1043
Document Type
Dissertation Defense
Degree Name
Doctor of Philosophy in Mechanical & Aerospace Engineering
College
College of Engineering
Department
Mechanical and Aerospace Engineering
First Advisor
Prof. Khalifa Harib
Keywords
Newton-Euler recursive formulation, dynamic modelling, kinematic modelling, quadruped, rigid-body dynamics, reaction wheel
Abstract
Despite advancements in legged robotics, comprehensive dynamic analyses remain limited in the literature. This research presents kinematic and dynamic modeling of a quadruped robot using the Newton-Euler approach to improve computational efficiency in high degree of freedom systems. The formulation leverages system over-constraints with assumed ground reaction forces and focuses on simulating two primary gait patterns: static walking and dynamic trotting. The research explores reaction wheel-based roll stabilization for a quadruped with 8 actuators, omitting the conventional Hip Abduction/Adduction (HAA) joints. This approach addresses roll control limitations by compensating for the reduced actuation. This research presents a brief overview of representative gaits for legged rovers, followed by a review of kinematic, dynamic, and control strategies for quadruped systems. The initial focus is on kinematic analysis of static walking gait using a planar model, with trajectories and gaits developed and simulated in MATLAB. Inverse kinematics and trajectory planning were performed and simulated in MATLAB to model the walking gait. Results matched expected outcomes and were experimentally validated on an 8-actuator quadruped, with all actuators mounted on the torso and Knee Flexion/Extension (KFE) motion transmitted via two four-bar linkage mechanisms. The main research models a 12-actuator quadruped with three actuators per leg, conducting full kinematic and dynamic analyses for staticwalking and dynamic trotting gaits. A flexible algorithm is developed to simulate the complete system dynamicsacross various gait patterns. The dynamic model is solved using the Newton-Euler recursive approach, computinglink forces and moments. Twelve generalized coordinates are used for static walking, with an additionalcoordinate for dynamic trotting. The framework employs programming strategies to solve six linear equations todetermine the unknown reaction forces at the legs. This approach effectively reduces the number of unknowns,thereby simplifying the computational complexity of the model. The robot’s body attitude is estimated from jointtrajectories, with velocity and acceleration derived from joint space variables. Forward dynamics is computedusing inverse dynamics to solve for joint accelerations via the mass matrix Coriolis, centrifugal and gravitationaltorque vectors. A reaction wheel, aligned with the primary axis, is integrated to generate compensatory torquesfor roll stabilization during dynamic trotting gait. The integrated approach, combining forward and inversedynamics with real-time roll stabilization via a reaction wheel, demonstrated effective, adaptive locomotion forquadruped systems. Experimental validation during static walking showed strong agreement between measuredand simulated torque profiles, with Hip Flexion/Extension (HFE) and Knee Flexion/Extension (KFE) joint torquesclosely matching trajectory predictions, confirming the model’s accuracy. These studies advance rigid-bodydynamic modeling by reducing system complexity through an efficient minimization of generalized coordinates.The proposed framework, incorporating both inverse and forward dynamics with reduced coordinates andsimplified ground constraints, significantly streamlines the overall dynamic formulation. The developedframework successfully implements gait-switching algorithms based on the robot’s current attitude. Thisresearch addresses key gaps in dynamic modeling, including computational efficiency, utilization of system over-constraints, and gait transition dynamics.
Included in
DYNAMIC ANALYSIS AND CONTROL OF A QUADRUPED ROBOTIC SYSTEM BASED ON NEWTON-EULER FORMULATION
F1, 1043
Despite advancements in legged robotics, comprehensive dynamic analyses remain limited in the literature. This research presents kinematic and dynamic modeling of a quadruped robot using the Newton-Euler approach to improve computational efficiency in high degree of freedom systems. The formulation leverages system over-constraints with assumed ground reaction forces and focuses on simulating two primary gait patterns: static walking and dynamic trotting. The research explores reaction wheel-based roll stabilization for a quadruped with 8 actuators, omitting the conventional Hip Abduction/Adduction (HAA) joints. This approach addresses roll control limitations by compensating for the reduced actuation. This research presents a brief overview of representative gaits for legged rovers, followed by a review of kinematic, dynamic, and control strategies for quadruped systems. The initial focus is on kinematic analysis of static walking gait using a planar model, with trajectories and gaits developed and simulated in MATLAB. Inverse kinematics and trajectory planning were performed and simulated in MATLAB to model the walking gait. Results matched expected outcomes and were experimentally validated on an 8-actuator quadruped, with all actuators mounted on the torso and Knee Flexion/Extension (KFE) motion transmitted via two four-bar linkage mechanisms. The main research models a 12-actuator quadruped with three actuators per leg, conducting full kinematic and dynamic analyses for staticwalking and dynamic trotting gaits. A flexible algorithm is developed to simulate the complete system dynamicsacross various gait patterns. The dynamic model is solved using the Newton-Euler recursive approach, computinglink forces and moments. Twelve generalized coordinates are used for static walking, with an additionalcoordinate for dynamic trotting. The framework employs programming strategies to solve six linear equations todetermine the unknown reaction forces at the legs. This approach effectively reduces the number of unknowns,thereby simplifying the computational complexity of the model. The robot’s body attitude is estimated from jointtrajectories, with velocity and acceleration derived from joint space variables. Forward dynamics is computedusing inverse dynamics to solve for joint accelerations via the mass matrix Coriolis, centrifugal and gravitationaltorque vectors. A reaction wheel, aligned with the primary axis, is integrated to generate compensatory torquesfor roll stabilization during dynamic trotting gait. The integrated approach, combining forward and inversedynamics with real-time roll stabilization via a reaction wheel, demonstrated effective, adaptive locomotion forquadruped systems. Experimental validation during static walking showed strong agreement between measuredand simulated torque profiles, with Hip Flexion/Extension (HFE) and Knee Flexion/Extension (KFE) joint torquesclosely matching trajectory predictions, confirming the model’s accuracy. These studies advance rigid-bodydynamic modeling by reducing system complexity through an efficient minimization of generalized coordinates.The proposed framework, incorporating both inverse and forward dynamics with reduced coordinates andsimplified ground constraints, significantly streamlines the overall dynamic formulation. The developedframework successfully implements gait-switching algorithms based on the robot’s current attitude. Thisresearch addresses key gaps in dynamic modeling, including computational efficiency, utilization of system over-constraints, and gait transition dynamics.