Impact at each leg transition is one of the main causes of energy dissipation in most of the current bipedal walking robots. Minimizing impact can reduce the energy loss. Instead of controlling the joint angle profiles to reduce the impact which requires significant amount of energy, installing elastic mechanisms on the robots structure is proposed in this research, enabling the robot to reduce the impact, and to store part of the energy in the elastic form which returns the energy to the robot. Practically, this motivates the development of the bipedal walking robots with adjustable stiffness elasticity which itself creates new challenging problems. This thesis addresses some of the challenges through five consecutive stages. Firstly, an adjustable compliant series elastic actuator (named ACSEA in this thesis) is developed. The velocity control mode of the electric motor is used to accurately control the output force of the ACSEA. Secondly, three different conceptual designs of the adjustable stiffness artificial tendons (ASAT) are proposed each of which is added at the ankle joint of a bipedal walking robot model. Simulation results of the collision phase (part of the gait between the heel-strike and the foot-touch-down in bipedal walking) demonstrate significant improvements in the energetics of the bipedal walking robot by proper stiffness adjustment of ASAT. In the third stage, in order to study the effects of ASATs on reducing the energy loss during the stance phase, a simplified model of bipedal walking is introduced consisting of a foot, a leg and an ASAT which is installed parallel to the ankle joint. A linear spring, with adjustable stiffness, is included in the model to simulate the generated force by the trailing leg during the double support phase. The concept of impulsive constraints is used to establish the mathematical model of impacts in the collision phase which includes the heel-strike and the foot-touch-down. For the fourth stage, an energy-feedback-based controller is designed to automatically adjust the stiffness of the ASAT which reduces the energy loss during the foot-touch-down. In the final stage, a speed tracking (ST) controller is developed to regulate the velocity of the biped at the midstance. The ST controller is an event-based time-independent controller, based on geometric progression with exponential decay in the kinetic energy error, which adjusts the stiffness of the trailing-leg spring to control the injected energy to the biped in tracking a desired speed at the midstance. Another controller is also integrated with the ST controller to tune the stiffness of the ASAT when reduction in the speed is desired. Then, the local stability of the system (biped and the combination of the above three controllers) is analyzed by calculating the eigenvalues of the linear approximation of the return map. Simulation results show that the combination of the three controllers is successful in tracking a desired speed of the bipedal walking even in the presence of the uncertainties in the leg’s initial angles. The outcomes of this research show the significant effects of adjustable stiffness artificial tendons on reducing the energy loss during bipedal walking. It also demonstrates the advantages of adding elastic elements in the bipedal walking model which benefits the efficiency and simplicity in regulating the speed. This research paves the way toward developing the dynamic walking robots with adjustable stiffness ability which minimize the shortcomings of the two major types of bipedal walking robots, i.e., passive dynamic walking robots (which are energy efficient but need extensive parameters tuning for gait stability) and actively controlled walking robots (which are significantly energy inefficient). / May 2008

Impact at each leg transition is one of the main causes of energy dissipation in most of the current bipedal walking robots. Minimizing impact can reduce the energy loss. Instead of controlling the joint angle profiles to reduce the impact which requires significant amount of energy, installing elastic mechanisms on the robots structure is proposed in this research, enabling the robot to reduce the impact, and to store part of the energy in the elastic form which returns the energy to the robot. Practically, this motivates the development of the bipedal walking robots with adjustable stiffness elasticity which itself creates new challenging problems. This thesis addresses some of the challenges through five consecutive stages. Firstly, an adjustable compliant series elastic actuator (named ACSEA in this thesis) is developed. The velocity control mode of the electric motor is used to accurately control the output force of the ACSEA. Secondly, three different conceptual designs of the adjustable stiffness artificial tendons (ASAT) are proposed each of which is added at the ankle joint of a bipedal walking robot model. Simulation results of the collision phase (part of the gait between the heel-strike and the foot-touch-down in bipedal walking) demonstrate significant improvements in the energetics of the bipedal walking robot by proper stiffness adjustment of ASAT. In the third stage, in order to study the effects of ASATs on reducing the energy loss during the stance phase, a simplified model of bipedal walking is introduced consisting of a foot, a leg and an ASAT which is installed parallel to the ankle joint. A linear spring, with adjustable stiffness, is included in the model to simulate the generated force by the trailing leg during the double support phase. The concept of impulsive constraints is used to establish the mathematical model of impacts in the collision phase which includes the heel-strike and the foot-touch-down. For the fourth stage, an energy-feedback-based controller is designed to automatically adjust the stiffness of the ASAT which reduces the energy loss during the foot-touch-down. In the final stage, a speed tracking (ST) controller is developed to regulate the velocity of the biped at the midstance. The ST controller is an event-based time-independent controller, based on geometric progression with exponential decay in the kinetic energy error, which adjusts the stiffness of the trailing-leg spring to control the injected energy to the biped in tracking a desired speed at the midstance. Another controller is also integrated with the ST controller to tune the stiffness of the ASAT when reduction in the speed is desired. Then, the local stability of the system (biped and the combination of the above three controllers) is analyzed by calculating the eigenvalues of the linear approximation of the return map. Simulation results show that the combination of the three controllers is successful in tracking a desired speed of the bipedal walking even in the presence of the uncertainties in the leg’s initial angles. The outcomes of this research show the significant effects of adjustable stiffness artificial tendons on reducing the energy loss during bipedal walking. It also demonstrates the advantages of adding elastic elements in the bipedal walking model which benefits the efficiency and simplicity in regulating the speed. This research paves the way toward developing the dynamic walking robots with adjustable stiffness ability which minimize the shortcomings of the two major types of bipedal walking robots, i.e., passive dynamic walking robots (which are energy efficient but need extensive parameters tuning for gait stability) and actively controlled walking robots (which are significantly energy inefficient).

Impact at each leg transition is one of the main causes of energy dissipation in most of the current bipedal walking robots. Minimizing impact can reduce the energy loss. Instead of controlling the joint angle profiles to reduce the impact which requires significant amount of energy, installing elastic mechanisms on the robots structure is proposed in this research, enabling the robot to reduce the impact, and to store part of the energy in the elastic form which returns the energy to the robot. Practically, this motivates the development of the bipedal walking robots with adjustable stiffness elasticity which itself creates new challenging problems. This thesis addresses some of the challenges through five consecutive stages. Firstly, an adjustable compliant series elastic actuator (named ACSEA in this thesis) is developed. The velocity control mode of the electric motor is used to accurately control the output force of the ACSEA. Secondly, three different conceptual designs of the adjustable stiffness artificial tendons (ASAT) are proposed each of which is added at the ankle joint of a bipedal walking robot model. Simulation results of the collision phase (part of the gait between the heel-strike and the foot-touch-down in bipedal walking) demonstrate significant improvements in the energetics of the bipedal walking robot by proper stiffness adjustment of ASAT. In the third stage, in order to study the effects of ASATs on reducing the energy loss during the stance phase, a simplified model of bipedal walking is introduced consisting of a foot, a leg and an ASAT which is installed parallel to the ankle joint. A linear spring, with adjustable stiffness, is included in the model to simulate the generated force by the trailing leg during the double support phase. The concept of impulsive constraints is used to establish the mathematical model of impacts in the collision phase which includes the heel-strike and the foot-touch-down. For the fourth stage, an energy-feedback-based controller is designed to automatically adjust the stiffness of the ASAT which reduces the energy loss during the foot-touch-down. In the final stage, a speed tracking (ST) controller is developed to regulate the velocity of the biped at the midstance. The ST controller is an event-based time-independent controller, based on geometric progression with exponential decay in the kinetic energy error, which adjusts the stiffness of the trailing-leg spring to control the injected energy to the biped in tracking a desired speed at the midstance. Another controller is also integrated with the ST controller to tune the stiffness of the ASAT when reduction in the speed is desired. Then, the local stability of the system (biped and the combination of the above three controllers) is analyzed by calculating the eigenvalues of the linear approximation of the return map. Simulation results show that the combination of the three controllers is successful in tracking a desired speed of the bipedal walking even in the presence of the uncertainties in the leg’s initial angles. The outcomes of this research show the significant effects of adjustable stiffness artificial tendons on reducing the energy loss during bipedal walking. It also demonstrates the advantages of adding elastic elements in the bipedal walking model which benefits the efficiency and simplicity in regulating the speed. This research paves the way toward developing the dynamic walking robots with adjustable stiffness ability which minimize the shortcomings of the two major types of bipedal walking robots, i.e., passive dynamic walking robots (which are energy efficient but need extensive parameters tuning for gait stability) and actively controlled walking robots (which are significantly energy inefficient).

In this thesis project, the possibility to make use of a mechanical spring to achieve stiffness adjustability in a shock absorber for mountain bikes is evaluated. A mechanical spring increases the shock absorber’s sensitivity compared to a fully adjustable air spring. Today, there are no mechanical springs available on the market that offer enough stiffness adjustment to suit different riders with large variation in weight. Therefore, a mechanical spring with a wide stiffness adjustment range could be ground-breaking if it is possible to implement in mountain bike shock absorbers. The work has been carried out in accordance with a product- and concept development approach where the final concept design has been optimised analytically and verified numerically. The developed spring has been integrated in a new damper design and the complete damper and spring system has been dimensioned to fit current mountain bike frames. The result is a prototype shock absorber with a spring to suit riders between 70-88kg. An alternative spring for cyclists between 59-75kg has also been proposed. Since these springs have been made to fit current mountain bikes, it was possible to conclude that a mechanical spring witha wide range of adjustable stiffness is feasible for mountain bike application. With available spring steels, it is not possible to accommodate every rider with only one spring. It is however possible to achieve adjustment that is suitable for a rider weight range of roughly 15-16kg. This is between 70-110% more than similar products available on the market can offer. / I detta examensarbete utvärderas möjligheten att använda en mekanisk fjäder för att uppnå justerbar fjäderstyvhet hos en stötdämpare avsedd för terrängcykling. En mekanisk fjäder ökar stötdämparens känslighet jämfört med en fullt justerbar luftfjäder. I dagsläget finns på marknadeningen mekanisk fjäder vilken kan erbjuda tillräcklig justeringsmån för att passa cyklister med stor viktvariation. Därför kan en mekanisk fjäder med ett brett styvhetsspann vara banbrytande om en sådan kan tillämpas på dagens terrängcyklar. Arbetet har utförts som ett produkt- och konceptutvecklingsprojekt där den slutliga konceptdesignen har optimerats analytiskt och verifierats numeriskt. Den fjäder som tagits fram har integrerats i en ny dämparkonstruktion och stötdämparsystemet har dimensionerats för att passa dagens terrängcyklar. Resultatet är en prototyp av en stötdämpare med en fjäder som passar cyklister mellan 70-88kg. En alternativ fjäder passande cyklister mellan 59-75kg har också tagits fram. Eftersom en justerbar fjäder vars design möjliggör användning i en stötdämpare för dagens terrängcyklar har slutsatsen dragits att en justerbar mekanisk fjäder kan fungera inom detta tillämpningsområde. Det är inte möjligt med dagens material att utforma en mekanisk fjäder med tillräckligt justerbar styvhet föratt passa alla åkare. Det är däremot möjligt att använda en fjäder som passar cyklister inom ett viktspann på omkring 15-17kg. Detta är mellan 70–110% mer än vad liknande produkter tillgängliga på marknaden idag kan erbjuda.