This paper introduces an accurate yet analytically simple approximation to the stance dynamics of the Spring-Loaded Inverted Pendulum (SLIP) model in the presence of non-negligible damping and non-symmetric stance trajectories. Since the SLIP model has long been established as an accurate descriptive model for running behaviors, its careful analysis is instrumental in the design of successful locomotion controllers. Unfortunately, none of the existing analytic methods in the literature explicitly take damping into account, resulting in degraded predictive accuracy when they are used for dissipative runners. We show that the methods we propose not only yield average predictive errors below 2% in the presence of significant damping, but also outperform existing alternatives to approximate the trajectories of a lossless model. Finally, we exploit both the predictive performance and analytic simplicity of our approximations in the design of a gait-level running controller, demonstrating their practical utility and performance benefits.

Control theory arose from a need to control synthetic systems. From regulating steam engines to tuning radios to devices capable of autonomous movement, it provided a formal mathematical basis for understanding the role of feedback in the stability (or change) of dynamical systems. It provides a framework for understanding any system with regulation via feedback, including biological ones such as regulatory gene networks, cellular metabolic systems, sensorimotor dynamics of moving animals, and even ecological or evolutionary dynamics of organisms and populations. Here, we focus on four case studies of the sensorimotor dynamics of animals, each of which involves the application of principles from control theory to probe stability and feedback in an organism's response to perturbations. We use examples from aquatic (two behaviors performed by electric fish), terrestrial (following of walls by cockroaches), and aerial environments (flight control by moths) to highlight how one can use control theory to understand the way feedback mechanisms interact with the physical dynamics of animals to determine their stability and response to sensory inputs and perturbations. Each case study is cast as a control problem with sensory input, neural processing, and motor dynamics, the output of which feeds back to the sensory inputs. Collectively, the interaction of these systems in a closed loop determines the behavior of the entire system.

Lateral stability of the spring-mass hopper suggests a two-step control strategy for running Chaos: An Interdisciplinary Journal of Nonlinear Science 19, 026106 (2009) In this paper, we analyze the self-stability properties of planar running with a dissipative springmass model driven by torque actuation at the hip. We first show that a two-dimensional, approximate analytic return map for uncontrolled locomotion with this system under a fixed touchdown leg angle policy and an open-loop ramp torque profile exhibits only marginal self-stability that does not always persist for the exact system. We then propose a per-stride feedback strategy for the hip torque that explicitly compensates for damping losses, reducing the return map to a single dimension and substantially improving the robust stability of fixed points. Subsequent presentation of simulation evidence establishes that the predictions of this approximate model are consistent with the behavior of the exact plant model. We illustrate the relevance and utility of our model both through the qualitative correspondence of its predictions to biological data as well as its use in the design of a task-level running controller. © 2010 American Institute of Physics. ͓doi:10.1063/1.3486803͔It has long been established that simple spring-mass systems, such as the well-studied spring-loaded inverted pendulum (SLIP) model, can accurately represent the dynamics of legged locomotion. However, the existing work in this domain almost exclusively focuses on lossless leg models with actuation through tunable leg stiffness, making it difficult to generalize associated results to physical systems. In this paper, we introduce a more realistic model with damping and actuation through a controllable hip torque, subsequently developing a sufficiently accurate analytic approximation to identify and characterize its limit cycles. We show that in the absence of any explicit controls, running with this model is only marginally stable, but when an "energy regulating" feedback law is introduced on the stance hip torque, an open-loop, fixed touchdown angle policy produces asymptotically stable running across a much larger range of states. We also show that the relatively understudied hip torque actuation not only provides robust stability properties, but also has interesting correspondence to data from biological runners, more accurately predicting horizontal ground reaction forces during locomotion.

Autonomous use of legged robots in unstructured, outdoor settings requires dynamically dexterous behaviors to achieve sufficient speed and agility without overly complex and fragile mechanics and actuation. Among such behaviors is the relatively under-studied pronking (aka. stotting), a dynamic gait in which all legs are used in synchrony, usually resulting in relatively slow speeds but long flight phases and large jumping heights. Instantiations of this gait for robotic systems have been mostly limited to open-loop strategies, suffering from severe pitch instability for underactuated designs due to the lack of active feedback. However, both the kinematic simplicity of this gait and its dynamic nature suggest that the Spring-Loaded Inverted Pendulum model (SLIP) would be a good basis for the implementation of a more robust feedback controller for pronking. In this paper, we describe how template-based control, a controller structure based on the embedding of a simple dynamical "template" within a more complex "anchor" system, can be used to achieve very stable pronking for a planar, underactuated hexapod robot. In this context, high-level control of the gait is regulated through speed and height commands to the SLIP template, while the embedding controller ensures the stability of the remaining degrees of freedom. We use simulation studies to show that unlike existing open-loop alternatives, the resulting control struc-M.M. Ankaralı Dept. of Electrical and Electronics Eng., Middle East Technical University, Ankara, Turkey e-mail: e134441@metu.edu.tr U. Saranlı ( ) Dept. of Computer Engineering, Bilkent University, Ankara, Turkey e-mail: saranli@cs.bilkent.edu.tr ture provides explicit gait control authority and significant robustness against sensor and actuator noise.

In this paper, we propose a new motion planning method that aims to robustly and computationally efficiently solve path planning and navigation problems for unmanned surface vehicles (USVs). Our approach is based on synthesizing two different existing methodologies: sequential composition of dynamic behaviours and rapidly exploring random trees (RRT). The main motivation of this integrated solution is to develop a robust feedback-based and yet computationally feasible motion planning algorithm for USVs. In order to illustrate the main approach and show the feasibility of the method, we performed simulations and tested the overall performance and applicability for future experimental applications. We also tested the robustness of the method under relatively extreme environmental uncertainty. Simulation results indicate that our method can produce robust and computationally feasible solutions for a broad class of USVs.