# Andy Ruina's research while affiliated with Cornell University and other places

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## Publications (94)

Horses stand for most of each day. Although they can use various leg configurations (postures), they usually stand with vertical legs. Why? We addressed this question with a 2D quasi-static model having three rigid parts: a trunk, massless fore-limbs and massless rear limbs, with hinges at the shoulders, hips, and hooves. The postural parameter we...

What is the effect of posture on the stability of a standing horse? We address this with a 2D quasi-static model. The model horse has 3 rigid parts: a trunk, a massless fore-limb and a massless rear limb, and has hinges at the shoulder, hip, and hooves. The postural parameter lg is the distance between the hooves. For a given lg, statics finds an e...

From which states and with what controls can a biped avoid falling or reach a given target state? What is the most robust way to do these? So as to help with the design of walking robot controllers, and perhaps give insights into human walking, we address these questions using two simple 2-D models: the inverted pendulum (IP) and linear inverted pe...

The energetic cost of transport for walking is highly sensitive to speed but relatively insensitive to changes in gravity level. Conversely, the cost of transport for running is highly sensitive to gravity level but not much to speed. Gait optimization with a minimally constrained bipedal model predicts a similar differential energetic response for...

We are designing a cheap, mass producible 1 m semi-autonomous robotic sailboat that can navigate the oceans for months using only intermittent external supervision. The boat should efficiently collect environmental data such as salinity, turbidity, fluorescence, and animal sounds. The boat has a symmetric airfoil sail, a thin, bulbed keel, and most...

We have experimented with and simulated Steinkamp's passive-dynamic hopper. This hopper cannot stand up (it is statically unstable), yet it can hop the length of a 5m 0.079 rad sloped ramp, with n ∼100 hops. Because, for an unstable periodic motion, a perturbation δx0 grows exponentially with the number of steps (δxn ∼ δx0 × λⁿ), where λ is the sys...

We are developing a robotic boat capable of sailing semi-autonomously for two years on the open ocean. Our design is a monohull sailboat with a weighted keel, no rudder, a controlled-angle sail, and an air-rudder to passively control the boats orientation relative to the wind without active control. We are working to optimize sail, keel and air-rud...

We present an approach to high-level control for bipedal walking exemplified with a 2D point-mass inextensible-legs inverted-pendulum model. Balance control authority here is only from step position and trailing-leg push-off, both of which are bounded to reflect actuator limits. The controller is defined implicitly as the solution of an optimizatio...

Before designing a controller in detail, we ask this question: for a given robot state, and every possible control action, what is the minimum number of steps needed to get to a given target state (if it is possible to do so)? Our biped model is a 2D inverted pendulum with massless legs. We have two controls: (i) the magnitude of an impulsive push-...

A bicycle or inverted pendulum can be balanced, that is kept nearly upright, by accelerating the base. This balance is achieved by steering on a bicycle. Simultaneously one can also control the lateral position of the base: changing of the track line of a bike or the position of hand under a balanced stick. We show here with theory and experiment t...

No legged walking robot yet approaches the high reliability and the low power usage of a walking person, even on flat ground. Here we describe a simple robot which makes small progress towards that goal. Ranger is a knee-less four-legged ‘bipedal’ robot which is energetically and computationally autonomous, except for radio controlled steering. Ran...

In some practical control problems of essentially continuous systems, the goal is not to tightly track a trajectory in state space, but only some aspects of the state at various points along the trajectory, and possibly only loosely. Here, we show examples in which classical discrete-control approaches can provide simple, low input-, and low output...

Extended abstract can be found here: http://www.cmu.edu/dynamic-walking/files/abstracts/Hasaneini_2013_DW.pdf
Watch the talk here: https://youtu.be/xIDSgtFDgcI?list=PLVqaARCrz-m9aFEsen8fkW4ZjdaFqRoGL

When two nominally rigid objects collide, their velocities change in response to the compression force between them. The difference in the normal component of the velocities of the objects is thus generally eliminated or reversed. The nature of collisions for nonrigid objects is more subtle. Surprisingly, when a long chain moving lengthwise collide...

A riderless bicycle can automatically steer itself so as to recover from falls. The common view is that this self-steering
is caused by gyroscopic precession of the front wheel, or by the wheel contact trailing like a caster behind the steer axis.
We show that neither effect is necessary for self-stability. Using linearized stability calculations a...

We have numerically found periodic collisionless motions of a walking model consisting of linked rigid objects. Unlike previous designs, this model can walk on level ground at noninfinitesimal speed with zero energy input. The model avoids collisional losses by using an internal mode of oscillation: swaying of the upper body coupled to the legs by...

Basic concepts on cohesive models and their usage in fracture are reviewed.These included potential based cohesive zone models and the concept of an anisotropic failure surface. Some new results are presented for history-dependent cohesive zone models. In particular, a class of cohesive zone models where damage is represented by a state variable wh...

A beer bottle or soda can on a table, when slightly tipped and released, falls to an upright position and then rocks up to a somewhat opposite tilt. Superficially this rocking motion involves a collision when the flat circular base of the container slaps the table before rocking up to the opposite tilt. A keen eye notices that the after-slap rising...

Even though human legs allow a wide repertoire of movements, when people travel by foot they mostly use one of two locomoto patterns, namely, walking and running. The selection of these two gaits from the plethora of options might be because walkin and running require less metabolic energy than other more unusual gaits. We addressed this possibilit...

We present canonical linearized equations of motion for the Whipple bicycle model consisting of four rigid laterally symmetri ideally hinged parts: two wheels, a frame and a front assembly. The wheels are also axisymmetric and make ideal knife-edg rolling point contact with the ground level. The mass distribution and geometry are otherwise arbitrar...

We have devised a simple, yet predictive model of the mechanics of both sculling and sweep rowing that reasonably mimics observed kinematic and force data. Our physical model is largely based upon the model proposed by Alexander [Alexander, F. H. (1925). The theory of rowing. In Proceedings of the University of Durham Philosophical Society (pp. 160...

Although people's legs are capable of a broad range of muscle-use and gait patterns, they generally prefer just two. They walk, swinging their body over a relatively straight leg with each step, or run, bouncing up off a bent leg between aerial phases. Walking feels easiest when going slowly, and running feels easiest when going faster. More unusua...

We have found periodic life-like brachiating motions of a rigid-body ape model that use no muscle or gravitational energy to move steadily forward. The most complicated of these models has 5 links (a body and two arms, each with 2 links) and 7 degrees of freedom in flight. The defining feature of all our periodic solutions is that all collisions ar...

Terrestrial legged locomotion requires repeated support forces to redirect the body's vertical velocity component from down to up. We assume that the redirection is accomplished by impulsive leg forces that cause small-angle glancing collisions of a point-mass model of the animal. We estimate the energetic costs of these collisions by assuming a me...

Here we present the design of a passive-dynamics based, fully autonomous, 3-D, bipedal walking robot that uses simple control, consumes little energy, and has human-like morphology and gait. Design aspects covered here include the freely rotating hip joint with angle bisecting mechanism; freely rotating knee joints with latches; direct actuation of...

Walking like an inverted pendulum reduces muscle-force and work demands during single support, but it also unavoidably requires mechanical work to redirect the body's center of mass in the transition between steps, when one pendular motion is substituted by the next. Production of this work exacts a proportional metabolic cost that is a major deter...

Passive-dynamic walkers are simple mechanical devices, composed of solid parts connected by joints, that walk stably down
a slope. They have no motors or controllers, yet can have remarkably humanlike motions. This suggests that these machines
are useful models of human locomotion; however, they cannot walk on level ground. Here we present three ro...

We describe simple one-dimensional models of passive (no energy input, no control), generally dissipative, vertical hopping and one- ball juggling. The central observation is that internal passive system motions can conspire to eliminate collisions in these systems. For hopping, two point masses are connected by a spring and the lower mass has inel...

Previous experiments [M. J. Coleman and A. Ruina, Phys. Rev. Lett. 80, 3658 (1998)] showed that a gravity-powered toy with no control and that has no statically stable near-standing configurations can walk stably. We show here that a simple rigid-body statically unstable mathematical model based loosely on the physical toy can predict stable limit-...

A person constrained to walk at a given speed v on a treadmill, chooses a particular step frequency f and step length d=v/f. Testing over a range of speeds generates a speed-frequency (v-f) relationship. This relationship is commonly posited as a basic feature of human gait. It is often further posited that this curve follows from minimum energy co...

Previous experiments [M. J. Coleman and A. Ruina, Phys. Rev. Lett. 80, 3658 (1998)] showed that a gravity-powered toy with no control and which has no statically stable near-standing configurations can walk stably. We show here that a simple rigid-body statically-unstable mathematical model based loosely on the physical toy can predict stable limit...

The authors have built the first three-dimensional, kneed, two-legged, passive-dynamic walking machine. Since the work of Tad McGeer in the late 1980s, the concept of passive dynamics has added insight into animal locomotion and the design of anthropomorphic robots. Various analyses and machines that demonstrate efficient human-like walking have be...

We address performance limits and dynamic behaviours of the two dimensional passive-dynamic bipedal walking mechanisms of Tad McGeer. The results highlight the role of heelstrike in determining the mechanical efficiency of gait, and point to ways of improving efficiency. We analyse several kneed and straight-legged walker designs, with round feet a...

Persons with gait abnormalities frequently undergo surgical procedures to improve the alignment of their limbs, increase the efficiency of movement, and prevent the progression of deformity (Bleck 1987; Gage 1991). For example, persons with cerebral palsy who walk with excessive flexion of the knees often have their hamstrings lengthened to increas...

In brachiation, an animal uses alternating bimanual support to move beneath an overhead support. Past brachiation models have been based on the oscillations of a simple pendulum over half of a full cycle of oscillation. These models have been unsatisfying because the natural behavior of gibbons and siamangs appears to be far less restricted than so...

We present a geometric representation of the set of 3D rigid body collisional impulses that are rea-sonably permissible by the combination of non-negative post-collision separation rate, non-negative collisional compression impulse, non-negative energy dissipation and the Coulomb friction inequality. The construction is presented for a variety of s...

We consider mechanical systems with intermittent contact that are smooth and holonomic except at the instants of transition. Overall such systems can be nonholonomic in that the accessible configuration space can have larger dimension than the instantaneous motions allowed by the constraints. The known examples of such mechanical systems are also d...

This paper addresses some performance limits of the kneed and
non-kneed passive-dynamic walking machines discovered by McGeer (1990).
Energetic inefficiency is measured by the slope γ needed to
sustain gait, with γ=0 being perfectly efficient. We show some
necessary conditions on the walker mass distribution to achieve
perfectly efficient walking....

Human walking can be approximated as a mechanical process governed by Newton's laws of motion, and not controlled. Tad McGeer first demonstrated, and we have confirmed, that a two-dimensional legged mechanism with four moving parts can exhibit stable, human-like walking on a range of shallow slopes with no actuation and no control (energy lost in f...

We demonstrate that an irreducibly simple, uncontrolled, two-dimensional, two-link model, vaguely resembling human legs, can walk down a shallow slope, powered only by gravity. This model is the simplest special case of the passive-dynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged at the hip, a point-mass at the hip,...

We built a simple two-leg toy that can walk stably with no control system. It walks downhill powered only by gravity. It seems to be the first McGeer-like passive-dynamic walker that is statically unstable in all standing positions, yet is stable in motion. It is one of a few known mechanical devices that are stable near a statically unstable confi...

PB 3000, 02015 TKK, Otakaari 5 A, Espoo, FINLAND 1 Introduction The stability of mechanisms is of natural interest to engineers and to students of nature's mechanisms. The most widely studied mechanisms are mechanical systems with conservative forces and which are only constrained by workless holonomic constraints. Such systems are Hamiltonian and,...

We describe a transducer system and analysis strategy that allows the determination of dynamic forces and moments applied by an arm-swinging animal during locomotion. We have employed readily available technology and analysis procedures to produce a low-cost but effective system. The solutions to several problems in the design of the system are pro...

We built a simple two-leg toy that can walk stably with no control system. It walks downhill powered only by gravity. It seems to be the first McGeer-like passive-dynamic walker that is statically unstable in all standing positions, yet is stable in motion. It is one of few known mechanical devices that are stable near a statically unstable configu...

This paper discusses the mechanics of a rigid rimless spoked wheel, or regular polygon, `rolling' downhill. By rolling, we mean motions in which the wheel pivots on one `support' spoke until another spoke collides with the ground, followed by transfer of support to that spoke, and so on. We carry out three-dimensional numerical and analytical stabi...

We present a simple new algebraic model with two restitution parameters for general 3D frictional single-point rigid-body collisions. The model is motivated by, and guaranteed to satisfy, basic restrictions on the collisional impulse. For disks and spheres, it becomes a bilinear model successfully used elsewhere. For general collisions, the predict...

Introduction Human motion is controlled by the neuro-muscular system. But bipedal walking, an example of a basic human motion, might be largely understood as a passive mechanical process [3]. For example, Tad McGeer demonstrated, by both computer simulation and physical model construction (both of which we have repeated), that a somewhat anthropomo...

We distinguish between, and discuss the applicability of, two levels of rigidity in rigid-body collision modeling. For rigidity in the strong,force-response, sense collisional contact deformations must be highly localized. The bodies then move according to second order rigid-body mechanics during the collision. Incremental collision laws and most c...

We report collision experiments with Delrin disks and a steel plate. The disks floated on an air table, and collided at low speeds with a thick plate clamped to the table. The collision angle was varied. The observed normal restitution was consistent with other studies. The frictional interaction differed from that reported for spheres and thick di...

We distinguish between, and discuss the applicability of, two levels of rigidity in rigid-body collision modeling.
For rigidity in the strong, force-response, sense collisional contact deformations must be highly localized. The bodies then move according to 2nd order rigid-body mechanics during the collision. Incremental collision laws and most col...

A discrete network of springs is used to model the failure of a craze in front of a crack under small-scale yielding conditions. The material outside the craze is assumed to be linearly isotropic elastic. Craze failure occurs when the first fibril ahead of the crack tip reaches the breaking force. The location of the craze-bulk interface is determi...

This paper discusses the mechanics of a rigid rimless spoked wheel, or regular polygon, ‘rolling’ downhill. By ‘rolling’, we mean motions in which the wheel pivots on one ‘support’ spoke until another spoke collides with the ground, followed by transfer of support to that spoke, and so on. We carry out three-dimensional (3D) numerical and analytica...

Polymer/polymer interfaces reinforced with block copolymers or grafted chains can fail by the pull-out of these chains. A number of constitutive models have been proposed in the literature to describe the pull-out of a single chain. In this paper, we use these models to construct a continuum theory of a weak interface, and we study the stability of...

In this paper, we study the relationship between crack nucleation and failure of an interface reinforced by chains and the results of a linear stability analysis presented in part 1 of this study (preceding paper in this issue). We develop a numerical procedure to simulate the deformation and failure of such an interface. We demonstrate that instab...

The problem of craze failure near the tip of a crack embedded inside a craze is investigated by modeling the crazed material as a highly anisotropic network of springs. This model is based on the presence of cross-tie fibrils in the craze microstructure. These cross-tie fibrils give the craze some small lateral load-bearing capacity so that they ca...

Compressive properties of elastic cellular solids are studied via experiments upon foam and upon single-cell models. Open-cell foam exhibits a monotonic stress-strain relation with a plateau region; deformation is localized in transverse bands. Single-cell models exhibit a force-deformation relation which is not monotonic. In view of recent concept...

The problem of craze failure near the tip of a crack embedded inside a craze is investigated in this work. Our micromechanics model is based on the presence of cross-tie fibrils in the craze microstructure. These cross-tie fibrils give the craze some small lateral load-bearing capacity so that they can transfer stress between the main fibrils. This...

Some problems in the dynamics of sliding of planar rigid bodies are treated by geometric methods based on the limit surface description of friction (S. Goyal, A. Ruina and J. Papadopoulos, Wear, 143 (1991) 307–330). The problems we consider, where the normal force is known a priori, have unique solutions although the friction force (and torque) may...

We present two geometric descriptions of the net frictional force and moment between a rigid body and a planar surface on which it slides. The limit surface, from classical plasticity theory, is the surface in load space which bounds the set of all possible frictional forces and moments that can be sustained by the frictional interface. Zhukovskii'...

We present a model which predicts seismological complexity even with no complexity in geometry or heterogeneity in material properties. Fault slip is numerically modeled using a Dieterich-type rate and state variable friction law at the planar interface of two infinitely long massless elastic slabs. A constant velocity boundary condition is imposed...

The authors present two geometric descriptions of the frictional
properties of a rigid body sliding on a planar surface. The limit
surface from classical plasticity theory, is the boundary of the set of
all possible frictional forces and moments that can be sustained by the
frictional interface. Zhukovskii's moment function is the frictional
moment...

Hart's constitutive law for inelastic deformation of metals in uniaxial loading is described. For sufficiently low temperature or high strain rates, Hart's constitutive law in uniaxial loading is accurately approximated by a simpler law termed the visco-plastic approximation. In the viscoplastic approximation Hart's “plastic” element reduces to a c...

Can a simple multi-block-spring model with total symmetry make interesting predictions for fault behaviour? Our model consists of a symmetric, slowly driven, two degree-of-freedom block-spring system with static/dynamic friction. The simple friction law and slow driving rate allow the state of this fourth order system to be described between slip e...

The 3 3 local mass matrix fully characterizes a pair of colliding \rigid" bodies for many purposes. We prove here that arbitrary 3 3, symmetric positive denite matrices have physical realizations as local mass matrices for collisions of two bodies with nite dimensions and inertia. General collision models thus must be able to handle all such matric...

The shear resistance of slipping surfaces at fixed normal stress is given by τ = τ(V, state). Here V is the slip velocity, dependence on “state” is equivalent to functional dependence with fading memory on prior V(t) and ∂τ(V, state)/∂V> 0. We establish linear stability conditions for steady slip states (V(t), τ(t) constant). For single degree-of-f...

The problem of magnetically induced eddy current flow in a thin cracked plate is posed and solved for a few special cases. The current density is singular at the tip of a nonconducting crack. The strength of this singularity, denoted M, is found by reducing the eddy current problem to a conduction problem and then using the mathematical methods of...

Singular terms in the crack tip elastic stress field of order r
-3/2, r
-5/2, ... are often neglected, thus rationalizing the use of the K field, r
-1/2, as the dominant term for fracture mechanics. We find the common explanation for neglecting the more singular terms in the series solution for the crack tip stress field unsatisfying. Further, the...

We consider quasistatic motion and stability of a single degree of freedom elastic system undergoing frictional slip. The system is represented by a block (slider) slipping at speed V and connected by a spring of stiffness k to a point at which motion is enforced at speed V0 We adopt rate and state dependent frictional constitutive relations for th...

The dependence of the friction on slip history is described by an experimentally motivated constitutive law where the friction is dependent on slip rate and state variables. The state variables are defined macroscopically by evolution equations for their rates of change in terms of their present values and slip rate. Experiments may strongly sugges...

The shear resistance of slipping surface at fixed normal stress is given by TAU=TAU (V, state). Here V = slip velocity, dependence on 'state' is equivalent to fuctional dependence with fading memory on prior V (t), and DELTATAU (V, state)/DELTAV0. Linear stability conditions were established for steady-slip states (V(t), TAU(t) constant). For singl...

## Citations

... Canted-in posture, also defined as abnormal compensatory posture [10,11]. In this posture the limbs are brought closer together under the trunk of the horse creating a non-vertical metacarpal/tarsal alignment. ...

... Rather, it is the ability for the legs to remain straight, and the muscles to do little to no work, while the body translates forward (Tucker, 1975;Griffin et al., 2004). Indeed, the reduction of gravity (which ought to provide less opportunity for transduction between these modes) changes energetic cost little in bipedal walking and results in a slight reduction in cost (Farley and McMahon, 1992;Hasaneini et al., 2017). Quadrupeds can emulate perfect transduction of gravitational and kinetic energy; the apparent energy "savings" in this case are not savings at all, but require costly simultaneous positive and negative work. ...

... Most prior models of human walking (e.g., [21,32,33]) address within-step "control," defined here as the processes that drive the dynamics of each step to remain viable (i.e., to prevent falling) [34]. While ensuring viability is indeed necessary to walk [35,36], it is not sufficient: humans engage in purposeful walking with a destination to reach and/or other tasks to achieve. Control models that "just walk" (i.e., remain viable) do not address how humans achieve such goal-directed walking. ...

... This property has been observed in some other legged systems too (see e.g. [23,24]). Second, in contrast to most mono-legged robots, we have assumed no flexibility condition; so the model cannot hop, albeit can do a handspring. ...

... The point-mass model enabled Hauser et al. to develop a controller that tracks the trajectory of a bicycle, while the bicycle is in an upright position [55]. Additionally, A. Sharma et al. used the point-mass model to develop a multivariable proportional controller for balancing a bicycle in a simulation environment [56]. In the work, a comparison between the Whipple model and the point-mass model is made as well. ...

... Therefore, they are considered a promising platform for the growing demand of long-term marine science activities (Silva et al., 2019). To date, dozens of distinctive autonomous sailing monohulls have been designed and are playing roles in multitudinous tasks (Neal, 2006;Augenstein et al., 2016;Baker et al., 2015;Meinig et al., 2015;De Robertis et al., 2019;Klinck et al., 2016). For autonomous sailing monohulls, speed performance is an important design consideration. ...

... Non-periodic walking conditions, however, require more compliance due to an unexpected timing of contact phase changes. Many walking controllers rely on swing leg compliance and contact force sensors to provide a phase-based or adaptive contact switch Pratt et al. (2012); Gehring et al. (2013); Kelly et al. (2016); Lim et al. (2001). Phase detection through contact force measurement helps to choose the right swing/stance controller for each leg which improves stability Aoi and Tsuchiya (2006) ;Faber and Behnke (2007); , despite a fixed timing in the desired periodic gait. ...

... Therefore, they are considered a promising platform for the growing demand of long-term marine science activities (Silva et al., 2019). To date, dozens of distinctive autonomous sailing monohulls have been designed and are playing roles in multitudinous tasks (Neal, 2006;Augenstein et al., 2016;Baker et al., 2015;Meinig et al., 2015;De Robertis et al., 2019;Klinck et al., 2016). For autonomous sailing monohulls, speed performance is an important design consideration. ...

Reference: Towards a general design