This work introduces a modular experimental platform for studying legged locomotion, constructed using the template-anchor methodology, which allows the generalization of designed applications to the broader spectrum of legged robots. A finite state machine governs the operation logic, enabling reliable phase-specific coordination within a hybrid dynamical system. Active hip torque control is integrated to stabilize trajectories and support continuous running, enhancing the dynamic capabilities of the platform. The experimental platform enables advanced system identification, forward prediction, and closed-loop control applications.

Widely accepted utility of simple spring-mass models for running behaviors as descriptive tools, as well as literal control targets, motivates accurate analytical approximations to their dynamics. Despite the availability of a number of such analytical predictors in the literature, their validation has mostly been done in simulation, and it is yet unclear how well they perform when applied to physical platforms. In this paper, we extend on one of the most recent approximations in the literature to ensure its accuracy and applicability to a physical monopedal platform. To this end, we present systematic experiments on a well-instrumented planar monopod robot, first to perform careful identification of system parameters and subsequently to assess predictor performance. Our results show that the approximate solutions to the spring-loaded inverted pendulum dynamics are capable of predicting physical robot position and velocity trajectories with average prediction errors of 2% and 7%, respectively. This predictive performance together with the simple analytic nature of the approximations shows their suitability as a basis for both state estimators and locomotion controllers.

Mobility through balancing on spherical wheels has recently received some attention in the robotics literature. Unlike traditional wheeled platforms, the operation of such platforms depends heavily on understanding and working with system dynamics, which have so far been approximated with simple planar models and their decoupled extension to three dimensions. Unfortunately, such models cannot capture inherently spatial aspects of motion such as yaw motion arising from the wheel rolling motion or coupled inertial effects for fast maneuvers. In this paper, we describe a novel, fully-coupled 3D model for such spherical wheeled platforms and show that it not only captures relevant spatial aspects of motion, but also provides a basis for controllers better informed by system dynamics. We focus our evaluations to simulations with this model and use circular paths to reveal advantages of this model in dynamically rich situations.

Practical realization of model-based dynamic legged behaviors is substantially more challenging than statically stable behaviors due to their heavy dependence on second-order system dynamics. This problem is further aggravated by the difficulty of accurately measuring or estimating dynamic parameters such as spring and damping constants for associated models and the fact that such parameters are prone to change in time due to heavy use and associated material fatigue. In this paper, we present an on-line, model-based adaptive control method for running with a planar spring-mass hopper based on a once-per-step parameter correction scheme. Our method can be used both as a system identification tool to determine possibly time-varying spring and damping constants of a miscalibrated system, or as an adaptive controller that can eliminate steady-state tracking errors through appropriate adjustments on dynamic system parameters. We present systematic simulation studies to show that our method can successfully accomplish both of these tasks.

The Spring-Loaded Inverted Pendulum (SLIP) model has long been established as an effective and accurate descriptive model for running animals of widely differing sizes and morphologies, while also serving as a basis for several hopping robot designs. Further research on this model led to the discovery of several analytic approximations to its normally nonintegrable dynamics. However, these approximations mostly focus on steady-state running with symmetric trajectories due to their linearization of gravitational effects, an assumption that is quickly violated for locomotion on more complex terrain wherein transient, non-symmetric trajectories dominate. In this paper, we introduce a novel gravity correction scheme that extends on one of the more recent analytic approximations to the SLIP dynamics and achieves good accuracy even for highly non-symmetric trajectories. Our approach is based on incorporating the total effect of gravity on the angular momentum throughout a single stance phase and allows us to preserve the analytic simplicity of the approximation to support our longer term research on reactive footstep planning for dynamic legged locomotion. We compare the performance of our method in simulation to two other existing analytic approximations and show that it outperforms them for most physically realistic non-symmetric SLIP trajectories while maintaining the same accuracy for symmetric trajectories.

The main driving force behind research on legged robots has always been their potential for high performance locomotion on rough terrain and the outdoors. Nevertheless, most existing control algorithms for such robots either make rigid assumptions about their environments (e.g flat ground), or rely on kinematic planning at low speeds. Moreover, the traditional separation of planning from control often has negative impact on the robustness of the system against model uncertainty and environment noise. In this paper, we introduce a new method for dynamic, fully reactive footstep planning for a simplified planar spring-mass hopper, a frequently used model for running behaviors. Our approach is based on a careful characterization of the model dynamics and an associated deadbeat controller, used within a sequential composition framework. This yields a purely reactive controller with a very large, nearly global domain of attraction that requires no explicit replanning during execution. Finally, we use a simplified hopper in simulation to illustrate the performance of the planner under different rough terrain scenarios and show that it is extremely robust to both model uncertainty and measurement noise.

We consider the design problem for a class of discrete-time and continuous-time neural networks. We obtain a characterization of all connection weights that store a given set of vectors into the network, that is, each given vector becomes an equilibrium point of the network. We also give sufficient conditions that guarantee the asymptotic stability of these equilibrium points.