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

Rapid acceleration of legged robots: a pneumatic approach

For robotics to be useful to the public in a multifaceted manner, they need to be both legged and agile. The legged constraint arises as many environments and systems in our world are tailored to ablebodied adults. Therefore, a practically useful robot would need to have the same morphology for maximum efficacy. For robots to be useful in these environments, they need to perform at least as well as humans, therefore presenting the agility constraint. These requirements have been out of reach of the field until recently. The aim of this thesis was to design a planar monopod robot for rapid acceleration manoeuvres, that could later be expanded to a planar quadruped robot. This was achieved through a hybrid electric and pneumatic actuation system. To this end, modelling schemes for the pneumatic cylinder were investigated and verified with physical experiments. This was done to develop accurate models of the pneumatic system that were later used in simulation to aid in the design of the platform. The design of the platform was aided through the use of Simulink to conduct iterative testing and multivariate evaluations using Monte Carlo simulation methods. Once the topology of the leg was set, the detail design was conducted in Solidworks and validated with its built in simulation functions. In addition to the mechanical design of the platform, a specialist boom was designed. The design needed to compensate for the forces the robot exerts on the boom as well as the material constraints on the boom. This resulted in the development of a cable-stayed, four bar mechanism boom system. An embedded operating system was created to control the robot and take in and fuse sensor inputs. This was run using multiple sensors, sub-controllers and microcontrollers. Sensor fusion for the system was done using a Kalman Filter to improve readings and estimate unmeasured states of the robot. This Kalman Filter took LiDAR and accelerometer readings as inputs to the system to produce a subcentimetre accurate position measure for the system. Finally, the completed platform was validated using fixed-body forward hopping tests. These tests showed a significant degree of similarity to the simulated results and therefore validated the design process

Optimal Control of the Cheetah During Rapid Manoeuvres

Cheetahs are incredibly fast, manoeuvrable and highly dynamic, but relatively little is understood about how this is achieved. Thus, understanding their abilities is a subject of research for roboticists and biologists. Trajectory optimisation is a tool often used to increase our understanding of cheetahs, but current approaches which handle the full complexity of poorly understood manoeuvres are slow. The lack of data means that there are no simulated models of cheetahs known to be representative of dynamic movements such as acceleration and turning. In this project, a modelling change is investigated that decreases the time to find trajectories for models involving long serial chains of rigid bodies. Leveraging this development, a software library is created which facilitates the process of finding trajectories of models of legged robots and animals. Using this library, a complex model of a cheetah is developed, based on real data and some experimentation. Finally, the model is used to generate high speed dynamic manoeuvres which present progress towards understanding the incredible abilities of cheetahs

Proof-of-concept of a 16-week foot muscle specific intervention programme on non-contact anterior cruciate ligament and lateral ankle sprain injury risk : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Sport & Exercise Science at Massey University, Manawatu, Palmerston North, New Zealand

During high-intensity sports where abrupt decelerations and unanticipated changes of direction are prevalent, impaired foot function is thought to play a role in increasing the risk for non-contact anterior cruciate ligament rupture (ACLR) and lateral ankle sprain (LAS) injury. The risk for sustaining an ACLR is linked to increased rearfoot eversion and excessive, dynamic subtalar joint pronation coupled with internal rotation of the shank, leading to a larger knee valgus angle, and increasing anterior cruciate ligament (ACL) strain under high loads. Impaired forefoot stability is linked to larger moment arm lengths around the ankle joint, increasing the risk for lateral ankle sprain (LAS) under high loads. Previous research has shown that dynamic foot function can influence ankle, knee, and hip movement. Increasing forefoot and medial longitudinal arch stiffness modulates the distal-to-proximal transfer of rotational movement in straight-line walking and running as well as low intensity change of direction tasks. Foot stiffness is created by both passive and active structure in the foot. Passive structures include the foot bones and -ligaments and work in conjunction with the plantar fascia to create stiffness and stability. The intrinsic and extrinsic muscles acting on the foot act in synergy to create stiffness actively. However, current prophylactic programmes do not aim to explicitly train the foot muscles. The aim of this project was thus to provide proof of concept for a foot muscle specific training intervention on dynamic foot function, as well as risk factors associated with ACLR and LAS injury. Establishing proof of concept provides valuable information for future large-scale randomised control studies investigating the integration of a foot muscle specific intervention in to ACLR and LAS injury prevention programmes. The overview of the functional anatomy of the foot in Chapter 2 described the bones that form the joints of the foot as well as the muscles that move the bones of the foot. The interaction of the segments of the foot is described as well as the way in which the foot is modelled. The chapter also provided the contextual evidence for exercise selection. Chapter 4 reviewed the literature and highlighted the relationship between dynamic, excessive subtalar joint pronation and rearfoot eversion to internal tibial rotation, the increase in the knee valgus angle and ACL strain. A link between instability of the forefoot and a larger hallux extension range of motion increasing risk for LAS is discussed. The review also discussed the effect of intrinsic and extrinsic foot muscles on movement of the foot segments and general foot function. A hypothesis was formed that a foot muscle specific intervention has the potential to influence dynamic foot function and risk factors associated with ACLR and LAS, supplementing current prophylactic programmes. Current literature does not definitively describe the coupling relationship between the segments of the lower limb nor the coupling between the segments of the foot during high-intensity unanticipated change of direction tasks. It is thus unknown whether training the foot muscles in an attempt to modulate the transfer of rotational forces from distal-to-proximal segments to decrease injury risk, is justified. A modified vector coding technique was adapted to describe and quantify the coordination patterns between the lower limb and foot segments, respectively. In Chapter 5 the literature regarding the modifications to the vector coding technique and its development from the continues relative phase method of describing movement relationship between objects was presented. The coupling relationship between the tri-planar calcaneus and transverse plane rotation of the shank during unanticipated change of direction tasks was described in Chapter 6. A distal-to-proximal coupling relationship between frontal- and transverse plane movement of the calcaneus and transverse plane rotation of the shank was established. The distal-proximal coupling between the calcaneus and shank suggested that shank rotation may be modulated by manipulating the frontal and transverse plane movement of the calcaneus. It thus seems worthwhile to investigate whether training the muscles that act on the foot would manipulate shank rotations and, in this way, decrease the strain on the ACL, reducing ACLR risk. In Chapter 7 the coupling relationship between the foot segments was described as it influences LAS risk. The forefoot was the only point of contact during unanticipated change of direction tasks. Throughout stance, an anti-phase coupling relationship in the form of metatarsal flexion coupled with calcaneus eversion, and metatarsal extension was coupled with calcaneus inversion. These coupling relationships indicated the importance of forefoot function in calcaneus control and potentially LAS risk. In the loading phase, metatarsal inversion was coupled with calcaneus inversion, potentially increasing LAS risk if metatarsal inversion was not limited. At maximum calcaneus inversion- and adduction velocities, both of which are associated with increased risk for LAS, hallux and metatarsal flexion accelerated. The increased forefoot flexion acceleration indicating the importance of the forefoot stiffness in creating forefoot stability, potentially influencing whole foot stiffness and lateral ankle stability during change of direction tasks. As the forefoot provides stiffness the foot is likely to be more stable and the rearfoot segments are free to move and align with the shank, potentially decreasing LAS risk. It seems thus important to investigate whether training the foot muscles will influence LAS risk. The 16-week progressive foot muscle specific intervention program was detailed in Chapter 8. Exercise components, selection and progression was described. The outcomes of the proof-of-concept study revealed that training the muscles acting on the foot show potential to resist the deformation of the medial longitudinal arch (MLA). Resistance to MLA deformation potentially played a role in the observed decrease of the maximum knee valgus angle, and ACLR risk factor, of the training group (TG). LAS injury risk factors, maximum ankle inversion angle and maximum ankle eversion moment arm length were also smaller for the group undergoing the intervention training. The decrease in the maximums of these LAS risk factors was potentially influenced by the increasing stiffness of the metatarsal anterior transverse arch (MetATA), which is likely to increase foot and ankle stability. Guidelines for future randomised controlled trials included variables to consider ensuring the groups are well matched before the intervention. A proposal regarding the methodology and implementation of an injury prevention programme as well as sample size recommendations were outlined. To ensure the groups are well matched before the intervention it would be prudent to match athletes for stance times, peak ground reaction forces (GRF) in addition to sport and body mass index (BMI). During data collection, the approach speed and thus the timing of the unanticipated change of direction task proved difficult to monitor and control, which potentially influenced the kinetic and kinematic outcomes of the pilot study. The TG also had low compliance to training which could have influenced the result of the intervention. Sample size calculations revealed that a sample size of 30 (falling within the recommended size for biomechanical studies) are needed to find significant differences in foot arch and foot segment angle variables. However, a larger number of athletes are needed per group to establish changes to ACLR and LAS risk variables. Functional anatomy and the coupling relationship between the segments of the lower limb and foot segments justified investigating the effect of foot muscle-specific intervention on ACLR and LAS risk factors. The pilot study revealed that training the muscles acting on the foot seem to influence foot function, but the effect on risk factors associated with ACLR and LAS is unclear. Following the guidelines as described in future randomised control trial is necessary to establish the effectiveness of integrating foot muscle-specific exercises into current ACLR and LAS prophylactic programmes