Bio-inspired swing leg control for spring-mass robots running on ground with unexpected height disturbance

Assessing the effects of foot strike patterns and shoe types on the control of leg length and orientation in running

This research investigates the stabilization of leg length and orientation during the landing phase of running, examining the effects of different footwear and foot strike patterns. Analyzing kinematic data from twenty male long-distance runners, both rearfoot and forefoot strikers, we utilized the Uncontrolled Manifold approach to assess stability. Findings reveal that both leg length and orientation are indeed stabilized during landing, challenging the hypothesis that rearfoot strikers exhibit less variance in deviations than forefoot strikers, and that increased footwear assistance would reduce these deviations. Surprisingly, footwear with a lower minimalist index enhanced post-landing stability, suggesting that cushioning contributes to both force dissipation and leg length stability. The study indicates that both foot strike patterns are capable of effectively reducing task-relevant variance, with no inherent restriction on flexibility for rearfoot strikers. However, there is an indication of potential reliance on footwear for stability. These insights advance our understanding of the biomechanics of running, highlighting the role of footwear in stabilizing leg length and orientation, which has significant implications for running efficiency and injury prevention.

Optimizing and designing a leg shape to increase robustness of a running robot on rough terrain

The superior ability of dynamic legged locomotion in traversing rough terrain relative to wheeled or tracked mechanisms comes with the cost of fragile stability. Simple control methods that use only a few basic detection sensors and apply a single controller help robots keep their balance when traversing unforeseen rough terrain. Exploiting multiple controllers simultaneously, such as the free leg length and stiffness in our hopping monopod, can further improve robustness but is often mechanically hard to implement. This work demonstrates that a curved leg shape can improve the robustness of a robot to perturbations in both terrain levels and initial horizontal velocity without complicating the control scheme. Our work develops spring loaded inverted pendulum (SLIP) based models that manifest the coupling of the leg's parameters and capture the rolling motion. We use these models to find an optimal combination of parameters that maximizes a measure for long-term stability-reaching a desired relative height above terrain. We demonstrate that when traversing unknown rough terrain, such optimal coupling can increase robustness to perturbations in the initial horizontal velocity by 93% relative to the optimal conventional SLIP model. We further demonstrate our results in experiments.

Effective locomotion at multiple stride frequencies using proprioceptive feedback on a legged microrobot

Limitations in actuation, sensing, and computation have forced small legged robots to rely on carefully tuned, mechanically mediated leg trajectories for effective locomotion. Recent advances in manufacturing, however, have enabled in such robots the ability for operation at multiple stride frequencies using multi-degree-of-freedom leg trajectories. Proprioceptive sensing and control is key to extending the capabilities of these robots to a broad range of operating conditions. In this work, we use concomitant sensing for piezoelectric actuation with a computationally efficient framework for estimation and control of leg trajectories on a quadrupedal microrobot. We demonstrate accurate position estimation (<16[Formula: see text] root-mean-square error) and control (<16[Formula: see text] root-mean-square tracking error) during locomotion across a wide range of stride frequencies (10 Hz-50 Hz). This capability enables the exploration of two bioinspired parametric leg trajectories designed to reduce leg slip and increase locomotion performance (e.g. speed, cost-of-transport (COT), etc). Using this approach, we demonstrate high performance locomotion at stride frequencies (10 Hz-30 Hz) where the robot's natural dynamics result in poor open-loop locomotion. Furthermore, we validate the biological hypotheses that inspired the trajectories and identify regions of highly dynamic locomotion, low COT (3.33), and minimal leg slippage (<10%).

Robust Bipedal Locomotion Based on a Hierarchical Control Structure

To improve biped locomotion’s robustness to internal and external disturbances, this study proposes a hierarchical structure with three control levels. At the high level, a foothold sequence is generated so that the Center of Mass (CoM) trajectory tracks a planned path. The planning procedure is simplified by selecting the midpoint between two consecutive Center of Pressure (CoP) points as the feature point. At the middle level, a novel robust hybrid controller is devised to drive perturbed system states back to the nominal trajectory within finite cycles without chattering. The novelty lies in that the hybrid controller is not subject to linear CoM dynamic constraints. The hybrid controller consists of two sub-controllers: an oscillation controller and a smoothing controller. For the oscillation controller, the desired CoM height is specified as a sine-shaped function, avoiding a new attractive limit cycle. However, this controller results in the inevitable chattering because of discontinuities. A smoothing controller provides continuous properties and thus can inhibit the chattering problem, but has a smaller region of attraction compared with the oscillation controller. A hybrid controller merges the two controllers for a smooth transition. At the low level, the desired CoM motion is defined as tasks and embedded in a whole body operational space (WBOS) controller to compute the joint torques analytically. The novelty of the low-level controller lies in that within the WBOS framework, CoM motion is not subject to fixed CoM dynamics and thus can be generalized.

Towards dynamic alternating tripod trotting of a pony-sized hexapod robot for disaster rescuing based on multi-modal impedance control

Hexapod robots are well suited for disaster rescuing tasks due to their stability and load capability. However, most current hexapod robots still rely on static gaits that largely limit their locomotion speed. This paper introduces a hierarchical control strategy to realize a dynamic alternating tripod trotting gait for a hexapod robot based on multi-modal impedance control. At the low level, a position-based impedance controller is developed to realize an adjustable compliant behavior for each leg. At the high level, a new gait controller is developed to generate a stable alternating tripod trotting gait, in which a gait state machine, a leg compliance modulation strategy, and a close-looped body attitude stabilizer are imposed. As a result, the alternating tripod trotting of the hexapod robot can be synchronized as the running of a bipedal robot with stable body attitude. Moreover, this control strategy was verified by experiments on a newly designed pony-sized disaster rescuing robot, HexbotIV, which successfully achieved a dynamic trotting gait with ability to resist the disturbances of mildly uneven terrains. Our control strategy as well as the experimental study can be a valuable reference for other hexapod robots and thus paves a way to the practical deployment of disaster rescuing robots.

A flight-phase terrain following control strategy for stable and robust hopping of a one-legged robot under large terrain variations

This work demonstrates a simple, once per step, flight-control method for robots running on a planar unknown rough-terrain environment. The robot used to exemplify these control strategies is the ParkourBot, a spring loaded inverted pendulum (SLIP)-based robot. The SLIP model is widely used for the description of humans and animals running motion and has been the basis for many robots. A known control scheme for increasing robustness of the conservative, SLIP model is the swing leg retraction (SLR) method. Despite of the SLR's popularity, it is not intended to be used on the more realistic, non-conservative damped SLIP model. On the damped SLIP model, the SLR controller failed to provide adequate results, therefore, we have derived a new simple, flight-phase control method called polynomial energy insertion (PEI). The new PEI method is based on the dead-beat solution of the damped simplified instantaneous SLIP (iSLIP) model, which assumes an infinitely stiff spring. Unlike the SLR which, starting from apex, changes the leg angle monotonically during flight, the PEI requires the leg length (hence, energy insertion) to change monotonically throughout the flight phase. Interestingly, the leg angle remains nearly constant. In simulations and experiments, we have compared the newly developed PEI to the previous SLR method. We have found that since the SLR does not control the horizontal velocity, it looses its stability under rough terrain. The PEI method was able to control the horizontal velocity and height from ground and hence showed great improvement in robustness to rough terrain. Moreover, in both simulations and experiments the PEI methods showed an increase in the mean jumps to failure of more than 30% compared to SLR-based controllers.

A model for differential leg joint function during human running

Locomotion requires coordination of leg joints to maintain stability and to maneuver. We studied leg joint function during constant-average-velocity running and the sagittal-plane maneuvers of step ascent and descent. We tested two hypotheses: (1) that leg joints perform distinct functions during locomotion; and (2) that humans select functional parameters to maximize intrinsic dynamic stability. We recorded whole-body kinematics and forces when participants stepped up or down a single vertical step, and found that leg joints show functional differences during both constant-average-velocity locomotion and maneuvers. The hip, knee and ankle function as a motor, damper, and spring, respectively. We therefore constructed a simplified computational model of a human leg with a motor, damper, and spring in series (MDS). The intrinsic dynamics of the model resulted in sustained locomotion on level ground within narrow parameter ranges. However, using parameters experimentally derived from humans, the model showed only short-term stability. Humans may not optimize intrinsic dynamic stability alone, but may instead choose mechanical and behavioral parameters appropriate for both constant-average-velocity locomotion and maneuvers. Understanding joint-level mechanical function during unsteady locomotion helps to understand how differential joint function contributes to whole-body performance, and could lead to improvements in rehabilitation, prosthetic and robotic design.

Arbitrary Symmetric Running Gait Generation for an Underactuated Biped Model

This paper investigates generating symmetric trajectories for an underactuated biped during the stance phase of running. We use a point mass biped (PMB) model for gait analysis that consists of a prismatic force actuator on a massless leg. The significance of this model is its ability to generate more general and versatile running gaits than the spring-loaded inverted pendulum (SLIP) model, making it more suitable as a template for real robots. The algorithm plans the necessary leg actuator force to cause the robot center of mass to undergo arbitrary trajectories in stance with any arbitrary attack angle and velocity angle. The necessary actuator forces follow from the inverse kinematics and dynamics. Then these calculated forces become the control input to the dynamic model. We compare various center-of-mass trajectories, including a circular arc and polynomials of the degrees 2, 4 and 6. The cost of transport and maximum leg force are calculated for various attack angles and velocity angles. The results show that choosing the velocity angle as small as possible is beneficial, but the angle of attack has an optimum value. We also find a new result: there exist biped running gaits with double-hump ground reaction force profiles which result in less maximum leg force than single-hump profiles.

Light level impacts locomotor biomechanics in a secondarily diurnal gecko, Rhoptropus afer

Locomotion through complex habitats relies on the continuous feedback from a number of sensory systems, including vision. Animals face a visual trade-off between acuity and light sensitivity that depends on light levels, which will dramatically impact the ability to process information and move quickly through a habitat, making ambient illumination an incredibly important ecological factor. Despite this, there is a paucity of data examining ambient light in the context of locomotor dynamics. There have been several independent transitions from the nocturnal ancestor to a diurnal activity pattern among geckos. We examined how ambient light level impacted the locomotor performance and high-speed three-dimensional kinematics of a secondarily diurnal, and cursorial, gecko (Rhoptropus afer) from Namibia. This species is active under foggy and sunny conditions, indicating that a range of ambient light conditions is experienced naturally. Locomotor speed was lowest in the 'no-light' condition compared with all other light intensities, occurring via a combination of shorter stride length and lower stride frequency. Additionally, the centre of mass was significantly lower, and the geckos were more sprawled, in the no-light condition relative to all of the higher light intensities. Locomotor behaviour is clearly sub-optimal under lower light conditions, suggesting that ecological conditions, such as very dense fog, might preclude the ability to run quickly during predator-prey interactions. The impact of ambient light on fitness should be explored further, especially in those groups that exhibit multiple transitions between diel activity patterns.

Don't break a leg: running birds from quail to ostrich prioritise leg safety and economy on uneven terrain

Cursorial ground birds are paragons of bipedal running that span a 500-fold mass range from quail to ostrich. Here we investigate the task-level control priorities of cursorial birds by analysing how they negotiate single-step obstacles that create a conflict between body stability (attenuating deviations in body motion) and consistent leg force–length dynamics (for economy and leg safety). We also test the hypothesis that control priorities shift between body stability and leg safety with increasing body size, reflecting use of active control to overcome size-related challenges. Weight-support demands lead to a shift towards straighter legs and stiffer steady gait with increasing body size, but it remains unknown whether non-steady locomotor priorities diverge with size. We found that all measured species used a consistent obstacle negotiation strategy, involving unsteady body dynamics to minimise fluctuations in leg posture and loading across multiple steps, not directly prioritising body stability. Peak leg forces remained remarkably consistent across obstacle terrain, within 0.35 body weights of level running for obstacle heights from 0.1 to 0.5 times leg length. All species used similar stance leg actuation patterns, involving asymmetric force–length trajectories and posture-dependent actuation to add or remove energy depending on landing conditions. We present a simple stance leg model that explains key features of avian bipedal locomotion, and suggests economy as a key priority on both level and uneven terrain. We suggest that running ground birds target the closely coupled priorities of economy and leg safety as the direct imperatives of control, with adequate stability achieved through appropriately tuned intrinsic dynamics.

Swing-leg trajectory of running guinea fowl suggests task-level priority of force regulation rather than disturbance rejection

To achieve robust and stable legged locomotion in uneven terrain, animals must effectively coordinate limb swing and stance phases, which involve distinct yet coupled dynamics. Recent theoretical studies have highlighted the critical influence of swing-leg trajectory on stability, disturbance rejection, leg loading and economy of walking and running. Yet, simulations suggest that not all these factors can be simultaneously optimized. A potential trade-off arises between the optimal swing-leg trajectory for disturbance rejection (to maintain steady gait) versus regulation of leg loading (for injury avoidance and economy). Here we investigate how running guinea fowl manage this potential trade-off by comparing experimental data to predictions of hypothesis-based simulations of running over a terrain drop perturbation. We use a simple model to predict swing-leg trajectory and running dynamics. In simulations, we generate optimized swing-leg trajectories based upon specific hypotheses for task-level control priorities. We optimized swing trajectories to achieve i) constant peak force, ii) constant axial impulse, or iii) perfect disturbance rejection (steady gait) in the stance following a terrain drop. We compare simulation predictions to experimental data on guinea fowl running over a visible step down. Swing and stance dynamics of running guinea fowl closely match simulations optimized to regulate leg loading (priorities i and ii), and do not match the simulations optimized for disturbance rejection (priority iii). The simulations reinforce previous findings that swing-leg trajectory targeting disturbance rejection demands large increases in stance leg force following a terrain drop. Guinea fowl negotiate a downward step using unsteady dynamics with forward acceleration, and recover to steady gait in subsequent steps. Our results suggest that guinea fowl use swing-leg trajectory consistent with priority for load regulation, and not for steadiness of gait. Swing-leg trajectory optimized for load regulation may facilitate economy and injury avoidance in uneven terrain.