Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Computer Science and Engineering

Major Professor

Luther R. Palmer, Ph.D.

Committee Member

Stephen Deban, Ph.D.

Committee Member

Rajiv Dubey, Ph.D.

Committee Member

Kyle Reed, Ph.D.

Committee Member

Yu Sun, Ph.D.


Passive dynamics, Self-stabilization, Terrain following


Terrestrial robots must be capable of negotiating rough terrain if they are to become autonomous outside of the lab. Although the control mechanism offered by wheels is attractive in its simplicity, any wheeled system is confined to relatively flat terrain. Wheels will also only ever be useful for rolling, while limbs observed in nature are highly multimodal. The robust locomotive utility of legs is evidenced by the many animals that walk, run, jump, swim, and climb in a world full of challenging terrain.

On the other hand, legs with multiple degrees of freedom (DoF) require much more complex control and precise sensing than wheels. Legged robotic systems are easily hampered by sensor noise and bulky control loops that prohibit the high-speed adaptation to external perturbations necessary for dynamic stability in real time. Low sensor bandwidth can limit the system’s reaction time to external perturbations. It is also often necessary to filter sensor data, which introduces significant delays in the control loop. In addition, state estimation is often relied upon in order to compute active stabilizing responses. State estimation requires accurate sensor data, often involving filtering, and can involve additional nontrivial computation such as the pseudo-inversion of fullbody Jacobians. This perception portion of the control burden is all incurred before a response can be planned and executed. These delays can prevent a system from executing a corrective response before instability leads to failure. The present work presents an approach to legged system design and control that reduces both the perception and planning aspects of the online control burden.

A commonly accepted design goal in robotics is to accomplish a task with the fewest possible DoF in order to tighten the control loop and avoid the curse of dimensionality. However, animals control many DoF in a manner that adapts to external perturbations faster than can be explained by efferent neural control. The passive mechanics of segmented animal limbs are capable of rejecting unexpected disturbances without the supervision of an active controller. By simulating biomimetic limbs, we can learn more about this preflexive response, how the properties of segmented biological limbs foster self-stable passive mechanics, and how the control burden can be mitigated in robotic legged systems.

The contribution of this body of work is to reduce the control burden of legged locomotion for robots by drawing on self-stabilizing mechanical design and control principles observed in animal locomotion. To that end, minimal templates such as Sensory-Coupled Action Switching

Modules (SCASM), Central Pattern Generators (CPGs), and the Spring-Loaded Inverted Pendulum (SLIP) model are used to learn more about the essential components of legged locomotion. The motivation behind this work lies largely in the study of how internal, predictive models and the intrinsic mechanical properties of biological limbs help animals self-stabilize in real time. Robotic systems have already begun to demonstrate the benefits of these biological design primitives in an engineering context, such as reduced cost of transportation and an immediate mechanical response that does not need to wait for sensor feedback or planning.

The original research presented here explores the extent to which these principles can be utilized in order to encourage stable legged locomotion over uneven terrain with as little sensory information as possible. A method for generating feedforward, terrain-adaptive control primitives based on a compliant limb architecture is developed. Offline analysis of system dynamics is used to develop clock-driven patterns of leg stiffness and attack angle control during late swing with which passive stance phase dynamics will produce the desired apex height and stride period to within 0.1 mm and 50 μs, respectively. A feedforward method of energy modulation is incorporated that regulates velocity to within 10−5 m/s. Preservation of a constant stride period eliminates the need for detection of the apex event. Precise predictive controls based on thorough offline dynamic modeling reduce the system’s reliance on state and environmental data, even in rough terrain. These offline models of system dynamics are used to generate a controller that predicts the dynamics of running over uneven terrain using an internal clock signal.

Real-time state estimation is a non-trivial bottleneck in the control of mobile systems, legged and wheeled alike. The present work significantly reduces this burden by generating predictive models that eliminate the need for state estimation within the control loop, even in the presence of damping. The resulting system achieves not only self-stable legged running, but direct control of height, speed, and stride period without inertial sensing or force feedback. Through this work, the controller dependency on accurate and rapid sensing of the body height and velocity, apex event, and ground variation was eliminated. This was done by harnessing physics-based models of leg dynamics, used to generate predictive controls that exploit the passive mechanics of the compliant limb to their full potential. While no real world system is entirely deterministic, such a predictive model may serve as the base layer for a lightweight control architecture capable of stable robotic limb control, as in animal locomotion.