A contact-implicit direct trajectory optimization scheme for the study of legged maneuverability

For legged robots to move safely in unpredictable environments, they need to be manoeuvrable, but transient motions such as acceleration, deceleration and turning have been the subject of little research compared to constant-speed gait. They are difficult to study for two reasons: firstly, the way they are executed is highly sensitive to factors such as morphology and traction, and secondly, they can potentially be dangerous, especially when executed rapidly, or from high speeds. These challenges make it an ideal topic for study by simulation, as this allows all variables to be precisely controlled, and puts no human, animal or robotic subjects at risk. Trajectory optimization is a promising method for simulating these manoeuvres, because it allows complete motion trajectories to be generated when neither the input actuation nor the output motion is known. Furthermore, it produces solutions that optimize a given objective, such as minimizing the distance required to stop, or the effort exerted by the actuators throughout the motion. It has consequently become a popular technique for high-level motion planning in robotics, and for studying locomotion in biomechanics. In this dissertation, we present a novel approach to studying motion with trajectory optimization, by viewing it more as “trajectory generation” – a means of generating large quantities of synthetic data that can illuminate the differences between successful and unsuccessful motion strategies when studied in aggregate. One distinctive feature of this approach is the focus on whole-body models, which capture the specific morphology of the subject, rather than the highly-simplified “template” models that are typically used. Another is the use of “contact-implicit” methods, which allow an appropriate footfall sequence to be discovered, rather than requiring that it be defined upfront. Although contact-implicit methods are not novel, they are not widely-used, as they are computationally demanding, and unnecessary when studying comparatively-predictable constant speed locomotion. The second section of this dissertation describes innovations in the formulation of these trajectory optimization problems as nonlinear programming problems (NLPs). This “direct” approach allows these problems to be solved by general-purpose, open-source algorithms, making it accessible to scientists without the specialized applied mathematics knowledge required to solve NLPs. The design of the NLP has a significant impact on the accuracy of the result, the quality of the solution (with respect to the final value of the objective function), and the time required to solve the proble