The role and implementation of compliance in legged locomotion

Many robots excel at precise positioning and trajectory tracking using software control, and most successful robotic applications utilize this ability—examples include CNC machining, robotic welding, painting, and pick-and-place circuit board assembly. The mechanical design of these robots focuses on rigid transmissions and minimizing compliance in the structure, so the software controller can accurately track a desired position as a function of time, regardless of any disturbance forces. However, there is a class of tasks for which rigid actuation is not ideal: physical interaction with the world, especially interaction that involves an impact or kinetic energy transfer. Animals tend to excel at these tasks, and far outperform the best robots. Examples include walking, running, catching a ball, gripping a piece of fruit firmly but without causing damage, and many types of assembly tasks. For dynamic behaviors such as running, the performance limitations of a robot are often due to limitations of the mechanical design. A robot is an integrated system of electronics, software, and mechanism, and each part of the system limits or enables the behavior of the whole. While some behaviors can easily be implemented through simple actuators and direct software control, a running machine requires mechanical design that is specialized for the task. Among other things, physical springs are essential for a robust and efficient running gait, to store energy, provide high mechanical power, and overcome bandwidth limitations of traditional actuators. An ideal kinematic design, where the joints and links are perfectly sized and placed for the desired task, and motors that exceed the force and speed requirements of the task are not sufficient for successful dynamic interactions. Inertia, transmission friction, and other dynamic effects have a significant role in the behavior of a robot. We are building running and walking machines with a focus on mechanical design to enable efficient and robust gaits. The defining characteristic of a running gait is spring-like behavior; all running animals, from small insects to large mammals, exhibit a center-of-mass motion that resembles a bouncing ball or a pogo stick. The spring-like behavior is implemented with the assistance of physical springy elements, such as tendons, and not entirely through software or neural control. Energy cycles back and forth between the ballistic trajectory of the body and the compression of the leg spring. To exhibit this behavior, our robots incorporate a mechanical spring that is tuned to absorb and release the energy of a running gait at the appropriate frequency. Electric motors act in series with this spring to add or remove energy from the cycle to modify or control the running gait. Our first prototype machine is a single actuator mounted to a bench, called the Actuator with Mechanically Adjustable Series Compliance, or AMASC. The stiffness and the no-load position of the joint are mechanical configurations that can be independently adjusted using two separate motors, and it is a test platform to verify and refine several design ideas for leg joints of running and walking robots. After significant testing and design revision, we incorporated the ideas behind the AMASC into the design of a full bipedal robot, the Biped with Mechanically Adjustable Series Compliance, or BiMASC. A single leg prototype of the BiMASC was constructed and tested, and after some final revisions, we have built the Electric Cable Differential (ECD) Leg. The ECD Leg derives its name from the construction—using electric motors, cable drives, and mechanical differentials to actuate the system. One ECD Leg, named Thumper, is assembled as a monopod and installed in our laboratory at the Robotics Institute to study the role of compliance in running gaits. Two ECD Legs are assembled as a biped named MABEL, which is installed in Professor Jessy Grizzle’s Laboratory at the University of Michigan and will serve as a platform to explore novel control ideas. In this thesis, we demonstrate that physical springs are extremely important for supporting a running gait. Additionally, through experiments on the ECD Leg, we demonstrate that there is an c © 2008 Jonathan W. Hurst i energetically optimal leg stiffness. The design and construction of the robots in this thesis are an exploration of methods for adjusting the leg stiffness to obtain the optimal stiffness for a running gait. The AMASC and BiMASC utilize co-contraction of antagonistic springs to tune the stiffness to a desired value. The ECD leg, in contrast, utilizes both active control of the motor and kinematic adjustments to control the stiffness behavior of the leg. We suggest that that co-contraction of antagonistic springs is energetically expensive, and that active control of a leg to modify its inherent stiffness might be energetically cheaper, with the same functionality. The ECD leg successfully hopped in place, as well as at speed. Thumper and MABEL demonstrate, for the first time, a cable drive paired with series elasticity for a running machine. The AMASC is the first demonstration of series elasticity implemented via a mechanical differential, and the BIMASC, Thumper, and MABEL all utilize this same concept. The mechanical design of the ECD leg contains many novel ideas that will be utilized in future walking and running machines. ii c © 2008 Jonathan W. Hurst