arXiv subjects

Ross L. Hatton

Publications and source records attributed to Ross L. Hatton.

30 records · Page 2Linked to original sources

arXiv2022

Motion Planning for Agile Legged Locomotion using Failure Margin Constraints

The complex dynamics of agile robotic legged locomotion requires motion planning to intelligently adjust footstep locations. Often, bipedal footstep and motion planning use mathematically simple models such as the linear inverted pendulum, instead of dynamically-rich models that do not have closed-form solutions. We propose a real-time optimization method to plan for dynamical models that do not have closed form solutions and experience irrecoverable failure. Our method uses a data-driven approximation of the step-to-step dynamics and of a failure margin function. This failure margin function is an oriented distance function in state-action space where it describes the signed distance to success or failure. The motion planning problem is formed as a nonlinear program with constraints that enforce the approximated forward dynamics and the validity of state-action pairs. For illustration, this method is applied to create a planner for an actuated spring-loaded inverted pendulum model. In an ablation study, the failure margin constraints decreased the number of invalid solutions by between 24 and 47 percentage points across different objectives and horizon lengths. While we demonstrate the method on a canonical model of locomotion, we also discuss how this can be applied to data-driven models and full-order robot models.

cs.RO↗

arXiv2022

Scales and Locomotion: Non-Reversible Longitudinal Drag

Locomotion requires that an animal or robot be able to move itself forward farther than it moves backward in each gait cycle (formally, that it be able to break the symmetry of its interactions with the world). Previous work has established that a difference between lateral and longitudinal drag provides sufficient conditions for locomotion to be possible. The geometric mechanics community has used this principle to build a geometric framework for describing the effectiveness and efficiency of undulatory locomotion. Researchers in biology and robotics have observed that structures such as snake scales additionally provide a difference between forward and backward longitudinal drag. As yet, however, the impact of scales on the geometric features relevant to locomotion effectiveness and efficiency have not yet been explored. We present a geometric model for a single-joint undulating system with scales and identify the features needed to understand its motion. Mathematically, the scales can be treated as inducing a "Finsler metric" on the configuration space, and this paper lays the groundwork for further research into application of such Finsler metrics to robotic locomotion.

cs.RO↗

arXiv2021

The Geometry of Optimal Gaits for Inertia-dominated Kinematic Systems

Isolated mechanical systems -- e.g., those floating in space, in free-fall, or on a frictionless surface -- are able to achieve net rotation by cyclically changing their shape, even if they have no net angular momentum. Similarly, swimmers immersed in "perfect fluids" are able to use cyclic shape changes to both translate and rotate even if the swimmer-fluid system has no net linear or angular momentum. Finally, systems fully constrained by direct nonholonomic constraints (e.g., passive wheels) can push against these constraints to move through the world. Previous work has demonstrated that the net displacement induced by these shape changes corresponds to the amount of *constraint curvature* that the gaits enclose. To properly assess or optimize the utility of a gait, however, we must also consider the time or resources required to execute it: A gait that produces a small displacement per cycle, but that can be executed in a short time, may produce a faster average velocity than a gait that produces a large displacement per cycle, but takes much longer to complete a cycle at the same average instantaneous effort. In this paper, we consider two effort-based cost functions for assessing the costs associated with executing these cycles. For each of these cost functions, we demonstrate that fixing the average instantaneous cost to a unit value allows us to transform the effort costs into time-to-execute costs for any given gait cycle. We then illustrate how the interaction between the constraint curvature and these costs leads to characteristic geometries for optimal cycles, in which the gait trajectories resemble elastic hoops distended from within by internal pressures.

cond-mat.soft↗

arXiv2021

Data-Driven Geometric System Identification for Shape-Underactuated Dissipative Systems

Systems whose movement is highly dissipative provide an opportunity to both identify models easily and quickly optimize motions. Geometric mechanics provides means for reduction of the dynamics by environmental homogeneity, while the dissipative nature minimizes the role of second order (inertial) features in the dynamics. Here we extend the tools of geometric system identification to ``Shape-Underactuated Dissipative Systems (SUDS)'' -- systems whose motions are more dissipative than inertial, but whose actuation is restricted to a subset of the body shape coordinates. Many animal motions are SUDS, including micro-swimmers such as nematodes and flagellated bacteria, and granular locomotors such as snakes and lizards. Many soft robots are also SUDS, particularly those robots using highly damped series elastic actuators. Whether involved in locomotion or manipulation, these robots are often used to interface less rigidly with the environment. We motivate the use of SUDS models, and validate their ability to predict motion of a variety of simulated viscous swimming platforms. For a large class of SUDS, we show how the shape velocity actuation inputs can be directly converted into torque inputs suggesting that systems with soft pneumatic actuators or dielectric elastomers can be modeled with the tools presented. Based on fundamental assumptions in the physics, we show how our model complexity scales linearly with the number of passive shape coordinates. This offers a large reduction on the number of trials needed to identify the system model from experimental data, and may reduce overfitting. The sample efficiency of our method suggests its use in modeling, control, and optimization in robotics, and as a tool for the study of organismal motion in friction dominated regimes.

cs.RO↗

arXiv2021

Learning Spring Mass Locomotion: Guiding Policies with a Reduced-Order Model

In this paper, we describe an approach to achieve dynamic legged locomotion on physical robots which combines existing methods for control with reinforcement learning. Specifically, our goal is a control hierarchy in which highest-level behaviors are planned through reduced-order models, which describe the fundamental physics of legged locomotion, and lower level controllers utilize a learned policy that can bridge the gap between the idealized, simple model and the complex, full order robot. The high-level planner can use a model of the environment and be task specific, while the low-level learned controller can execute a wide range of motions so that it applies to many different tasks. In this letter we describe this learned dynamic walking controller and show that a range of walking motions from reduced-order models can be used as the command and primary training signal for learned policies. The resulting policies do not attempt to naively track the motion (as a traditional trajectory tracking controller would) but instead balance immediate motion tracking with long term stability. The resulting controller is demonstrated on a human scale, unconstrained, untethered bipedal robot at speeds up to 1.2 m/s. This letter builds the foundation of a generic, dynamic learned walking controller that can be applied to many different tasks.

cs.RO↗

arXiv2020

Optimal Gaits for Drag-dominated Swimmers with Passive Elastic Joints

In this paper, we identify optimal swimming strategies for drag-dominated swimmers with a passive elastic joint. We use resistive force theory (RFT) to obtain the dynamics of the system. We then use frequency domain analysis to relate the motion of the passive joint to the motion of the actuated joint. We couple this analysis with elements of the geometric framework introduced in our previous work aimed at identifying useful gaits for systems in drag dominated environments, to identify speed-maximizing and efficiency-maximizing gaits for drag-dominated swimmers with a passive elastic joint.

physics.bio-ph↗

arXiv2020

Planning for the Unexpected: Explicitly Optimizing Motions for Ground Uncertainty in Running

We propose a method to generate actuation plans for a reduced order, dynamic model of bipedal running. This method explicitly enforces robustness to ground uncertainty. The plan generated is not a fixed body trajectory that is aggressively stabilized: instead, the plan interacts with the passive dynamics of the reduced order model to create emergent robustness. The goal is to create plans for legged robots that will be robust to imperfect perception of the environment, and to work with dynamics that are too complex to optimize in real-time. Working within this dynamic model of legged locomotion, we optimize a set of disturbance cases together with the nominal case, all with linked inputs. The input linking is nontrivial due to the hybrid dynamics of the running model but our solution is effective and has analytical gradients. The optimization procedure proposed is significantly slower than a standard trajectory optimization, but results in robust gaits that reject disturbances extremely effectively without any replanning required.

cs.RO↗

arXiv2018

A Data-Driven Approach to Connection Modeling

The study of motion in animals and robots has been aided by insights from geometric mechanics. In friction dominated systems, a mechanical "connection" can provide a high fidelity mechanical model. The connection is a co-vector (Lie algebra) valued map on the configuration space of the system. As such, empirically estimating a global model of the connection requires a truly exhaustive collection of experiments, and is thus prohibitive on all systems with even a moderate number of degrees of freedom. In this work, insights from data driven oscillator theory enable us to define a framework for estimating a local model of a connection in the vicinity of observed animal and robot gait cycles. The estimates are produced directly from motion capture data of a stochastically perturbed cyclic behavior. We demonstrate the model extraction process under noisy, experiment-like conditions by simulating planar multi-segment serpentine swimmers in a low Reynolds number (viscous-friction) environment. Following this, we assess model accuracy in the presence of observation error. Validating our method's capability to produce accurate models in the presence of simulated system and observational noise motivates its usage on real robotic and biological systems.

physics.bio-ph↗

arXiv2016

Soap-bubble Optimization of Gaits

In this paper, we present a geometric variational algorithm for optimizing the gaits of kinematic locomoting systems. The dynamics of this algorithm are analogous to the physics of a soap bubble, with the system's Lie bracket supplying an "inflation pressure" that is balanced by a "surface tension" term derived from a Riemannian metric on the system's shape space. We demonstrate this optimizer on a variety of system geometries (including Purcell's swimmer) and for optimization criteria that include maximizing displacement and efficiency of motion for both translation and turning motions.

math.OC↗

arXiv2016

A review on locomotion robophysics: the study of movement at the intersection of robotics, soft matter and dynamical systems

In this review we argue for the creation of a physics of moving systems -- a locomotion "robophysics" -- which we define as the pursuit of the discovery of principles of self generated motion. Robophysics can provide an important intellectual complement to the discipline of robotics, largely the domain of researchers from engineering and computer science. The essential idea is that we must complement study of complex robots in complex situations with systematic study of simplified robophysical devices in controlled laboratory settings and simplified theoretical models. We must thus use the methods of physics to examine successful and failed locomotion in simplified (abstracted) devices using parameter space exploration, systematic control, and techniques from dynamical systems. Using examples from our and other's research, we will discuss how such robophysical studies have begun to aid engineers in the creation of devices that begin to achieve life-like locomotor abilities on and within complex environments, have inspired interesting physics questions in low dimensional dynamical systems, geometric mechanics and soft matter physics, and have been useful to develop models for biological locomotion in complex terrain. The rapidly decreasing cost of constructing sophisticated robot models with easy access to significant computational power bodes well for scientists and engineers to engage in a discipline which can readily integrate experiment, theory and computation.

cs.RO↗

arXiv2014

Sidewinding with minimal slip: Snake and robot ascent of sandy slopes

Limbless organisms such as snakes can navigate nearly all terrain. In particular, desert-dwelling sidewinder rattlesnakes (Crotalus cerastes) operate effectively on inclined granular media (such as sand dunes) that induce failure in field-tested limbless robots through slipping and pitching. Our laboratory experiments reveal that as granular incline angle increases, sidewinder rattlesnakes increase the length of their body in contact with the sand. Implementing this strategy in a physical robot model of the snake enables the device to ascend sandy slopes close to the angle of maximum slope stability. Plate drag experiments demonstrate that granular yield stresses decrease with increasing incline angle. Together, these three approaches demonstrate how sidewinding with contact-length control mitigates failure on granular media.

physics.bio-ph↗

arXiv2013

Geometric visualization of self-propulsion in a complex medium

Combining geometric mechanics theory, laboratory robotic experiment and numerical simulation, we study the locomotion in granular media (GM) of the simplest non-inertial swimmer, the Purcell three-link swimmer. Using granular resistive force laws as inputs, the theory relates translation and rotation of the body to shape changes (movements of the links). This allows analysis, visualization, and prediction of effective movements that are verified by experiment. The geometric approach also facilitates comparison between swimming in GM and in viscous fluids.

cond-mat.soft↗