A long-standing argument in model-based control of locomotion is about the level of complexity that a model should have to define a behavior such as running. Even though a goldilocks model based on biomechanical evidence is often sought, it is unclear what level of complexity qualifies to be such a model. This dilemma deepens further for bipedal robotic running with point feet, since these robots are underactuated. When center-of-mass (COM) trajectories defined by the spring-loaded inverted pendulum (SLIP) model are fully tracked, angular coordinates of the robot's trunk become uncontrolled. Existing work in the literature approach this problem either by trading off COM trajectory tracking against upright trunk posture during stance or by adopting more detailed models that include effects of trunk angular dynamics. In this paper, we present a new approach based on modifying foot placement targets of the SLIP model. Theoretical analysis and numerical results show that the proposed approach can be alternative to existing strategies.

Existing research on dynamically capable legged robots, particularly those based on spring-mass models, generally considers improving in isolation either the stability and control accuracy on the rough terrain, or the energetic efficiency in steady state. In this paper, we propose a new method to address both, based on the hierarchical embedding of a simple spring-loaded inverted pendulum (SLIP) template model with a tunable radial damping coefficient into a realistic leg structure with series-elastic actuation. Our approach allows using the entire stance phase to inject/remove energy both for transient steps and in steady state, decreasing the maximum necessary actuator power while eliminating wasteful sources of the negative work. In doing so, we preserve the validity of the existing analytic approximations to the underlying SLIP model, propose improvements to increase the predictive accuracy, and construct accurate, model-based controllers that use the tunable damping coefficient of the template model. We provide extensive comparative simulations to establish the energy and power efficiency advantages of our approach, together with the accuracy of model-based gait control methods.

Spring-mass models have been very successful both in describing and generating running behaviors. Control of system energy within these models takes different forms, among which the use of a linear actuator in series with the leg spring has been preferred by many recent monopedal and bipedal platform designs due to its relative robustness and simplicity. However, the validity of the well-known Spring-Loaded Inverted Pendulum (SLIP) model of running for such platforms can only preserved under a specific family of control strategies to drive the actuator. In this paper, we propose a novel controller in this family, based on the idea of embedding a lossy SLIP template with a tunable damping coefficient into the linearly actuated compliant leg system. We show that this maximizes energy input within a single stride, allows decreased power requirements on the actuator compared to alternative methods, while preserving the validity and accuracy of analytic solutions and model-based controllers. We present systematic simulations to establish performance gains with respect to the commonly investigated method of modulating leg stiffness. Enabling the most efficient use of actuator power in this manner while preserving analytic tractability will allow efficient and accurate control of running for linearly actuated compliant leg designs.

Electrical motors are often used to actuate mechanisms with varying speed and under varying load e.g., missile control actuation systems or robot extremities. Sizing of the motor is critical in these applications where space is limited. Varying speed and load cause poor utilization of the motor if the reduction ratio is constant. This requires employment of a larger motor than the smallest possible with ideal variable transmission. To realize better utilization of the motor, we propose a series elastic actuator that works as a load sensitive continuously variable transmission system. This is achieved by combining a pin in slot mechanism with an elastic output shaft. The proposed mechanism is modeled and simulated using example missile flight data and a typical robot finger loading scenario. Results are compared to the constant reduction ratio case, and advantages of the proposed mechanism are shown as decreased actuator size and power.