Bipedal robotic locomotion based on passive dynamics is a field that has been extensively researched. By exploiting the natural dynamics of the system, these bipedal robots consume less energy and require minimal control to take a step. Yet the design of most of these bipedal machines is inherently unstable and difficult to control since there is a tendency for the machine to fall once it stops walking. This thesis presents the design and analysis of a novel three-legged walking robot for a single step. The STriDER (Self-excited Tripedal Dynamic Experimental Robot) incorporates aspects of passive dynamic walking into a stable tripedal platform. During a step, two legs act as stance legs while the other acts as a swing leg. A stance plane, formed by the hip and two ground contact points of the stance legs, acts as a single effective stance leg. When viewed in the sagittal plane, the machine can be modeled as a planar four link pendulum. To initiate a step, the legs are oriented to push the center of gravity outside of the stance legs. As the body of the robot falls forward, the swing leg naturally swings in between the two stance legs and catches the STriDER. Once all three legs are in contact with the ground, the robot regains its stability and the posture of the robot is then reset in preparation for the next step. To guide the design of the machine, a MATLAB simulation was written to allow for tuning of several design parameters, including the mass, mass distribution, and link lengths. Further development of the code also allowed for optimization of the design parameters to create an ideal gait for the robot. A self-excited method of actuation, which seeks to drive a stable system toward instability, was used to control the robot. This method of actuation was found to be robust across a wide range of design parameters and relatively insensitive to controller gains. / Master of Science

For robotic manipulation tasks in uncertain environments, research typically revolves around developing the best possible software control strategy. However, the passive dynamics of the mechanical system, including inertia, stiffness, damping and torque limits, often impose performance limitations that cannot be overcome with software control. Discussions about the passive dynamics are often imprecise, lacking comprehensive details about the physical limitations. In the first half of this paper, we develop relationships between an actuator's passive dynamics and the resulting performance, to better understanding how to tune the passive dynamics. We characterize constant-contact physical interaction tasks into two different tasks that can be roughly approximated as force control and position control and calculate the required input to produce a desired output. These exact solutions provide a basis for understanding how the parameters of the mechanical system affect the overall system's bandwidth limit without limitations of a specific control algorithm. We then present our experimental results compared to the analytical prediction for each task using a bench top actuator. Our analytical and experimental results show what, until now, has only been intuitively understood: soft systems are better at force control, stiff systems are better at position control, and there is no way to optimize an actuator for both tasks. / Graduation date: 2012

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.

This thesis covers the study of an actively assisted passive walker with discontinuous and impulsive actuation. The dynamics of the passive and active portions are derived, and a comprehensive mathematical model is proposed. An actuation method is also proposed to study the use of multiple discrete actuation events in a walking gait. Two key cases are considered: actuation at the stance point and at the EA point of a non-kneed walker. An experimental walker was designed that is capable of passive walking and has an experimental implementation of the proposed actuation system. A thorough characterization of the model is then performed, with experimental validation to show that: at high ramp angles, energy injection results in an increase in BOA of ~38% on a stable walking gait at a Ct of 0.086, and at low ramp angles, injection results in a stride length increase of ~29% at a Ct of 0.06.

The field of autonomous walking robots has been dominated by the trajectory-control approach, which rigidly dictates joint angle trajectories at the expense of both energy efficiency and stability, and the passive dynamics approach, which uses no actuators, relying instead on natural mechanical dynamics as the sole source of control. Although the passive dynamics approach is energy efficient, it lacks the ability to modify gait or adapt to disturbances. Recently, minimally actuated walkers, or dynamic walkers, have been developed that use hip or ankle actuators---knees are always passive---to regulate mechanical energy variations through the timely application of joint torque pulses. Despite the improvement minimal actuation has provided, energy efficiency remains below target values and perturbation rejection capability (i.e., stability) remains poor. In this dissertation, we develop and analyze a simplified robotic system to assess biologically inspired methods of improving energy efficiency and stability in dynamic walkers. Our system consists of a planar, dynamically swinging leg with hip and knee actuation. Neurally inspired, nonlinear oscillators provide closed-loop control without overriding the leg's natural dynamics. We first model the passive stiffness of muscles by applying stiffness components to the joints of a hip-actuated swinging leg. We then assess the effect active knee control has on unperturbed and perturbed leg swinging. Our results indicate that passive joint stiffness improves energy efficiency by reducing the actuator work required to counter gravitational torque and by promoting kinetic energy transfer between the shank and thigh. We also found that active knee control 1) is detrimental to unperturbed leg swinging because it negatively affects energy efficiency while producing minimal performance improvement and 2) is beneficial during perturbed swinging because the perturbation rejection improvement outweighs the reduction in energy efficiency. By analyzing the effects of applying passive joint stiffness and active knee control to dynamic walkers, this work helps to bridge the gap between the performance capability of trajectory-control robots and the energy-efficiency of passive dynamic robots.

For their inherent stability and simple dynamics of motion, wheeled robots are very common in robotics applications. Many highly complex robots are being developed in research laboratories, but wheeled robots remain the most used robot in real-world situations. One of the most significant downfalls of wheeled robots is their inability to navigate over large obstacles or steps without assistance. A wheeled robot is capable of climbing steps that are no larger than the radius of the robot's tires, but steps larger than this are impassable by simply rolling over the object. Active systems that have been designed for use on wheeled robots to lift the robot over a step are effective, but are generally not easily implemented on a range of robotic platforms. Also, the additional size, cost, and power required for the additional actuators is a major drawback to these options. A solution to these problems is a novel, passive dynamic system that is inertially excited by the motion of the robot to allow the robot to rotate on each axle and "hop" over the step. The system that was investigated for this project is a sliding mass-spring that shifts forward and backward based on the acceleration of the base robot. With high acceleration, the mass is pushed towards the rear wheel from an inertial force and compresses a spring that creates a moment on the body to induce rotation. This torque can cause the robot to "pop a wheelie", lifting its front wheels off the ground. To pull the rear wheels up, the inertial force from a large deceleration of the robot shifts the mass forward and extends a spring. These effects result in a moment acting in the opposite direction that can rotate the robot on its front axle and pull the rear wheels up. By coordinating the acceleration and deceleration of the robot, the front wheels can lift over a step and the rear wheels can be pulled up afterward — both actions being a product of inertial actuation. This passive system does not need additional actuators or direct control of the sliding mass, so it can be more durable over a robot's lifetime. Other advantages of this system are that the design is simple, cost-effective, and can be adjusted and retrofit to a different wheeled robot in the future with little effort. By deriving the equations of motion of this inertially actuated sliding mass, the dynamics show how design parameters of the system can be tuned to better optimize the overall step-climbing process. A computer simulation was created to visualize the robotic step-climbing process and demonstrate the effects of changing design parameters. An implementation of this sliding mass system was added to a wheeled robot, and the results from experiments were compared to simulated trials. This research has shown that an inertially actuated sliding mass can effectively enable a wheeled robot to climb a step that was previously impassable and that the system can be tuned for other wheeled robots using an understanding of the system dynamics. / Master of Science

Human gait is elegant and efficient in propelling the body forward. While a healthy human gait is symmetric, any deviation from symmetry can cause inefficiencies to the entire body. Such asymmetries may present themselves in hemiplegic patients, prosthetic users, lower limb injuries, limb height and weight discrepancies, or abnormal overground foot rolling. In this dissertation, practical passive methods to alleviate such asymmetric walking dynamics are presented. The novel concepts presented in this manuscript can all be related and applied to passive gait rehabilitation, that is, the rehabilitation of a person's gait through methods that do not require external power. One of the passive rehabilitation solutions for asymmetric gait is the the Gait Enhancing Mobile Shoe (GEMS). The GEMS is designed to mimic the motions of a split-belt treadmill, which is commonly used for asymmetric gait rehabilitation. Two iterations of the GEMS prototype are presented. While the first development design of the GEMS was too bulky, it showed controlled and constant backward motion. The second fully mechanical design was tested on healthy participants and was successful in producing spatial and temporal aftereffects similar to those seen in split-belt treadmill gait studies. In order to more accurately define the dynamics of the GEMS wheel as an individual steps on the shoe, mathematical models that predict the static and dynamic behavior of irregularly shaped curves on a flat plane as a weight is applied are derived and verified. While this kinetic shape concept can be applied to rolling irregularly shaped wheels, it can also be utilized to predict and manipulate roll-over motions of human feet, prosthetic feet, or even robotic biped feet. This kinetic shape concept was applied to develop a force dependent musical string instrument, transportation device, a more efficient walking crutch for controlled crutch walking, and a unique form of force mathematics. The asymmetric kinematics of dissimilar human limbs can be synchronized for symmetry with a generalized passive kinematic synchronization technique that can match the motion of two or more dissimilar and uncoupled rotating systems. This kinematic synchronization technique introduced in this dissertation can be applied to duplicate the motion of swinging human limbs with dissimilar masses and mass distributions, which allows for the passive synchronization and rehabilitation of human limbs such as swinging arms and legs during walking. This technique also allows for the synchronization of mechanical systems such as pendulums, propellers, or rotating cams. Finally, a detailed derivation of a two and three link passive dynamic walker (PDW) model with and without variable radius feet is presented. While PDW models have been studied and derived for decades, this dissertation offers a clear and complete guide on how to derive the kinematics and kinetics of the simplest compass gait, three-link point-foot, and for the first time, a variable radius foot PDW model, where the roll-over foot shape of the PDW can be dependent on its position or other kinematic variables. This advancement in the PDW model allows for the systematic evaluation of the change of various gait parameters such as foot roll-over shape or robotic foot dynamics. This numerical biped model was compared to human gait parameters. This comparison included normal walking, tied- and split-belt treadmill walking, and GEMS walking. This model was also used to analyze the dynamic effects of changing the foot roll-over parameters such as foot roll radius and foot shape curvature. In addition, the PDW model was employed to investigate the perception of normal and pathological gait. The PDW model was systematically manipulated to produce walking patterns that showed a degree of abnormality in spatial and temporal gait parameters. This analysis showed that certain gait parameters may be asymmetrically changed to some extent without causing an abnormal perception.