Legged robots have the potential to be a valuable technology that provides agile and adaptive locomotion over complex terrain. To realize legged locomotion's full abilities a control design must consider the nonlinear piecewise dynamics of the systems. This paper aims to develop a controller for the planar bounding of a quadrupedal robot.
The bounding of the quadruped robot is characterized by a simplified hybrid model that consists of two subsystems for stance and flight phases and the switching laws between the two states. An additional model, the Multibody model, with fewer simplifications, is used concurrently to best approximate real-world behavior. The bounding gait (periodic orbit) of the robot is predicted by an optimization method based on the numerical integration of the differential equations of subsystems. To stabilize the gait, a switching controller is applied which can be split into two separate phases: stance-phase and swing-phase control. The stance phase implements reaction force control utilizing a body state feedback controller and a gait stabilizer, while the swing phase deploys position control in conjunction with a trajectory planning algorithm to ensure proper footfall. Numerical simulations are carried out for the system with/without control. The control strategy is further validated by simulations of the Simscape multibody model. The overall simulated controller results are promising and demonstrate stable bounding for four system cycles.
","abstract_html":"<p>Legged robots have the potential to be a valuable technology that provides agile and adaptive locomotion over complex terrain. To realize legged locomotion's full abilities a control design must consider the nonlinear piecewise dynamics of the systems. This paper aims to develop a controller for the planar bounding of a quadrupedal robot.</p> <p>The bounding of the quadruped robot is characterized by a simplified hybrid model that consists of two subsystems for stance and flight phases and the switching laws between the two states. An additional model, the Multibody model, with fewer simplifications, is used concurrently to best approximate real-world behavior. The bounding gait (periodic orbit) of the robot is predicted by an optimization method based on the numerical integration of the differential equations of subsystems. To stabilize the gait, a switching controller is applied which can be split into two separate phases: stance-phase and swing-phase control. The stance phase implements reaction force control utilizing a body state feedback controller and a gait stabilizer, while the swing phase deploys position control in conjunction with a trajectory planning algorithm to ensure proper footfall. Numerical simulations are carried out for the system with/without control. The control strategy is further validated by simulations of the Simscape multibody model. The overall simulated controller results are promising and demonstrate stable bounding for four system cycles.</p>","abstract_has_math":false,"creators":["Ward, Patrick John"],"institution":null,"degree_name":"MS in Mechanical Engineering","degree_level":null,"degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Siyuan Xing","Mechanical Engineering","College of Engineering"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-06-01T07:00:00Z","date_published":"2022-06-01T07:00:00Z","updated_at":"2026-07-24T01:32:29Z","subjects":["Control","Robot","Bounding","Quadruped","Orbit","Simscape","Acoustics, Dynamics, and Controls","Navigation, Guidance, Control, and Dynamics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.15368/theses.2022.70"],"render_values":[{"text":"10.15368/theses.2022.70","href":"https://doi.org/10.15368/theses.2022.70","code":true}]}]},"links":{"outbound_url":"https://digitalcommons.calpoly.edu/theses/2624","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Siyuan Xing","Mechanical Engineering","College of Engineering"]},{"key":"dc:creator","label":"Author","values":["Ward, Patrick John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2022-06-10T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS in Mechanical Engineering"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Control","Robot","Bounding","Quadruped","Orbit","Simscape","Acoustics, Dynamics, and Controls","Navigation, Guidance, Control, and Dynamics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.calpoly.edu/theses/2624","10.15368/theses.2022.70"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Legged robots have the potential to be a valuable technology that provides agile and adaptive locomotion over complex terrain. To realize legged locomotion's full abilities a control design must consider the nonlinear piecewise dynamics of the systems. This paper aims to develop a controller for the planar bounding of a quadrupedal robot.
The bounding of the quadruped robot is characterized by a simplified hybrid model that consists of two subsystems for stance and flight phases and the switching laws between the two states. An additional model, the Multibody model, with fewer simplifications, is used concurrently to best approximate real-world behavior. The bounding gait (periodic orbit) of the robot is predicted by an optimization method based on the numerical integration of the differential equations of subsystems. To stabilize the gait, a switching controller is applied which can be split into two separate phases: stance-phase and swing-phase control. The stance phase implements reaction force control utilizing a body state feedback controller and a gait stabilizer, while the swing phase deploys position control in conjunction with a trajectory planning algorithm to ensure proper footfall. Numerical simulations are carried out for the system with/without control. The control strategy is further validated by simulations of the Simscape multibody model. The overall simulated controller results are promising and demonstrate stable bounding for four system cycles.
"]},{"key":"dc:title","label":"Title","values":["Modeling and Control of a Planar Bounding Quadrupedal Robot"]}]}],"canonical_facts":{"dc:contributor":["Siyuan Xing","Mechanical Engineering","College of Engineering"],"dc:creator":["Ward, Patrick John"],"dc:date.available":["2022-06-10T07:00:00Z"],"dc:description.abstract":["Legged robots have the potential to be a valuable technology that provides agile and adaptive locomotion over complex terrain. To realize legged locomotion's full abilities a control design must consider the nonlinear piecewise dynamics of the systems. This paper aims to develop a controller for the planar bounding of a quadrupedal robot.
The bounding of the quadruped robot is characterized by a simplified hybrid model that consists of two subsystems for stance and flight phases and the switching laws between the two states. An additional model, the Multibody model, with fewer simplifications, is used concurrently to best approximate real-world behavior. The bounding gait (periodic orbit) of the robot is predicted by an optimization method based on the numerical integration of the differential equations of subsystems. To stabilize the gait, a switching controller is applied which can be split into two separate phases: stance-phase and swing-phase control. The stance phase implements reaction force control utilizing a body state feedback controller and a gait stabilizer, while the swing phase deploys position control in conjunction with a trajectory planning algorithm to ensure proper footfall. Numerical simulations are carried out for the system with/without control. The control strategy is further validated by simulations of the Simscape multibody model. The overall simulated controller results are promising and demonstrate stable bounding for four system cycles.
"],"dc:identifier":["https://digitalcommons.calpoly.edu/theses/2624","10.15368/theses.2022.70"],"dc:subject":["Control","Robot","Bounding","Quadruped","Orbit","Simscape","Acoustics, Dynamics, and Controls","Navigation, Guidance, Control, and Dynamics"],"dc:title":["Modeling and Control of a Planar Bounding Quadrupedal Robot"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_name":["MS in Mechanical Engineering"]},"updated_at":"2026-07-24T01:32:29Z"}