Support Polygon Research Articles

Gait planning and adjustment for a hexapod walking robot with one leg failure

ABSTRACT Gait adjusting is an effective way to solve leg failure problems and is also the foundation of intelligent self-adjustment. This paper takes a hexagonal type of robot as a prototype and proposes a ‘2-2-1’ gait grouping and gait sequence for the one leg failure case based on the ‘4 + 2’ gait. The longitudinal stability margin is used to evaluate the FLF-A and FLF-B gaits with left front leg failure and FLM-A and FLM-B gait with left middle leg failure. The foothold positions are adjusted by changing the median angle of the stance phase of the body-coxa joint in each leg in order to make sure the centre of gravity is in a stable support polygon. The experiments of the robot walking show that the FLF-A gait and the FLM-B gait are more stable than the FLF-B and FLM-A after adjustment. The pitch and roll angles are maintained within − 3° to 3°, which verify the effectiveness of the stance phase leg median position adjustment strategy. This study could be used to do forward pre-adjustment in the case of one leg failure.

Learning to Walk with Adaptive Feet

In recent years, tasks regarding autonomous mobility favoredthe use of legged robots rather than wheeled ones thanks to their higher mobility on rough and uneven terrains. This comes at the cost of more complex motion planners and controllers to ensure robot stability and balance. However, in the case of quadrupedal robots, balancing is simpler than it is for bipeds thanks to their larger support polygons. Until a few years ago, most scientists and engineers addressed the quadrupedal locomotion problem with model-based approaches, which require a great deal of modeling expertise. A new trend is the use of data-driven methods, which seem to be quite promising and have shown great results. These methods do not require any modeling effort, but they suffer from computational limitations dictated by the hardware resources used. However, only the design phase of these algorithms requires large computing resources (controller training); their execution in the operational phase (deployment), takes place in real time on common processors. Moreover, adaptive feet capable of sensing terrain profile information have been designed and have shown great performance. Still, no dynamic locomotion control method has been specifically designed to leverage the advantages and supplementary information provided by this type of adaptive feet. In this work, we investigate the use and evaluate the performance of different end-to-end control policies trained via reinforcement learning algorithms specifically designed and trained to work on quadrupedal robots equipped with passive adaptive feet for their dynamic locomotion control over a diverse set of terrains. We examine how the addition of the haptic perception of the terrain affects the locomotion performance.

Portable Support Polygon Measurement System in Walking Aid Supported Gait

Portable Support Polygon Measurement System in Walking Aid Supported Gait

Implications of Stabilometric Assessment in Determining Functional Deficits in Patients with Severe Knee Osteoarthritis: Observational Study.

Background: Osteoarthritis is one of the most frequent joint disorders in the world. The specialists in the field strongly support the role of physical exercise as a key component in the holistic management of arthrosis. The aim of the current study was to identify and assess the functional deficit of these patients and to identify means to alleviate it through pre-surgery physiotherapy programs. Methods: The study was conducted on two samples of patients: a witness sample, encompassing 126 subjects without pathologies at the level of their lower limbs, and a study sample, formed of 116 subjects diagnosed with severe gonarthrosis with total knee arthroplasty indication. The assessment protocol was accomplished with the GPS 400 stabilometric platform. Results: The barycenter differences within the support polygon, recorded for the two samples within sagittal deviation, emphasize that the barycenter shifting mainly towards the healthy lower limb will demand, from the individual, more intense rebalancing postural reactions that will place the center-of-gravity projection in the sagittal plane, closer to the central area of the support polygon. Conclusions: In the case of gonarthrosis and other joint disorders, the use of functional testing to assess body weight distribution and center-of-gravity imbalances represents a promising direction in the research on and management of these disorders, providing essential information for functional diagnosing and thus enabling the elaboration and monitoring of individualized functional rehabilitation plans.

Passive Lower Limb Exoskeleton for Kneeling and Postural Transition Assistance With Expanded Support Polygon

Passive Lower Limb Exoskeleton for Kneeling and Postural Transition Assistance With Expanded Support Polygon

ASPECTS REGARDING STATIC STABILITY AND DYNAMIC STABILITY OF THE TOWER CRANES

Tower cranes are widely used in construction works, because they are used to mechanize the works. Specialized for tall constructions, tower cranes have proven to be the most economical type of cranes. They are used for loading-unloading, transport and assembly operations on civil and industrial construction sites and their characteristics vary within very wide limits. Stability is an important indicator when sizing cranes. The stability condition requires that the resultant of the vertical forces be inside the support polygon, or, in other words, the load on all the bases should acquire positive values. The present paper presents some aspects related to static stability and then a study on the dynamic stability of tower cranes. The case of dynamic stability in transient regimes will be analyzed on a concrete case of a tower crane, followed by an analysis of the stability to wind and earthquake for these types of lifting machines.

Visual feedback influences the consistency of the locomotor pattern in Asian elephants (Elephas maximus).

Elephants are atypical of most quadrupeds in that they maintain the same lateral sequence footfall pattern across all locomotor speeds. It has been speculated that the preservation of the footfall patterns is necessary to maintain a statically stable support polygon. This should be a particularly important constraint in large, relatively slow animals. This suggests that elephants must rely on available sensory feedback mechanisms to actively control their massive pillar-like limbs for proper foot placement and sequencing. How the nervous system of elephants integrates the available sensory information for a stable gait is unknown. Here we explored the role that visual feedback plays in the control of the locomotor pattern in Asian elephants. Four Asian elephants (Elephas maximus) walked with and without a blindfold as we measured their stride time intervals. Coefficient of variation was used to assess changes in the overall variability of the stride time intervals, while approximate entropy was used to measure the stride-to-stride consistency of the time intervals. We show that visual feedback plays a role in the stride-to-stride consistency of the locomotor pattern in Asian elephants. These results suggest that elephants use visual feedback to correct and maintain proper sequencing of the limbs during locomotion.

Model Predictive Leg Configuration Control for Leg/Wheel Mobile Robots that Adapts to Changes in Ground Level

Leg/wheel mobile robots, which have articulated legs ending in a wheel, can walk on legs as well as drive on wheels by switching between those two motive mechanisms in response to the terrain. However, effective control of the redundant degrees of freedom of leg/wheel mobile robots is complex. In this study, we propose a model predictive controller for leg configuration control that achieves both driving along the ground surface and climbing over a step. The proposed method simultaneously optimizes the robot pose, wheel positions, and joint angles. To consider the kinematic configuration of the legs explicitly, we formulate constraints on the relative position between the body and wheels. The ground contact condition of the wheels is approximately expressed as a continuous function with respect to each wheel’s relative position to the ground. This formulation induces smooth lifting of the wheels when the ground level abruptly changes, as when climbing a step. To prevent overturning, we evaluate the load distribution between each grounded wheel and constrain the body position to form a support polygon consisting of the grounded wheels. We conducted numerical simulations to verify that the proposed method achieves both driving on wheels and climbing over a step.

Proactive Body Joint Adaptation for Energy-Efficient Locomotion of Bio-Inspired Multi-Segmented Robots

Typically, control strategies for legged robots have been developed to adapt their leg movements to deal with complex terrain. When the legs are extended in search of ground contact to support the robot body, this can result in the center of gravity (CoG) being raised higher from the ground and can lead to unstable locomotion if it deviates from the support polygon. An alternative approach is body adaptation, inspired by millipede/centipede locomotion behavior, which can result in low ground clearance and stable locomotion. In this study, we propose novel proactive neural control with online unsupervised learning, allowing multi-segmented, legged robots to proactively adapt their body to follow the surface contour and maintain efficient ground contact. Our approach requires neither kinematics nor environmental models. It relies solely on proprioceptive sensory feedback and short-term memory, enabling the robots to deal with complex 3D terrains. In comparison to traditional reflex-based control, our approach results in smoother and more energy-efficient robot locomotion on terrains with concave and convex curves or slopes of varying degrees in both simulation and real-world implementation.

Heuristic algorithms for the special knapsack packing problem with defects arising in aircraft arrangement

This paper addresses a special knapsack packing problem in which identical pieces are packed into an irregular board with unusable regions to maximize the number of pieces. This problem arises from a real-world application in which the aircraft is placed on the carrier’s deck to maximize the number of aircraft. We propose the support polygon concept to solve one of the challenges of the problem, i.e., ensure that the support points inside the piece’s interior are located within the board when the piece protrudes from the board. Many strategies for determining the piece’s location and selecting the rotation angle of the piece are proposed and compared. Based on these techniques, we propose a deterministic heuristic algorithm to solve the problem. In addition, we develop an improved version of the algorithm, called the recursive search heuristic algorithm, to get higher-quality solutions. Many experiments were conducted to test the performance of different combinations of strategies and the proposed algorithms. The computational results show that the proposed algorithms have a strong capacity for obtaining good solutions, and updating many of the best results in the benchmark instances provided by the literature.

Motion characteristics and gait planning methods analysis for the walkable lunar lander to optimize the performances of terrain adaptability

Lunar environmental adaptability and gait control are significant for developing a walkable lunar lander (WLL). However, gait planning for the WLL is challenging due to the optimization process required for the stable margin sequence. To overcome this concern, this study develops a new Center of Gravity (COG) trajectory planning algorithm appropriate for a WLL that will enhance walking performance. Specifically, our method designs an adaptive back-stepping controller (ABSC) based on the established kinematic model to compensate for the influence of parameter uncertainties on the single-leg motion system. Compared to the classic PID control, our method's motion trajectory accuracy on the joint drive position is improved by 3.2 times. Additionally, various experiments on the prototype device verify the foot's motion trajectory. Furthermore, a new COG trajectory planning algorithm is proposed that combines the Jacobian COG and the centroid of a support polygon, including a foot contact constraint. This strategy effectively balances optimization and search operations, improving the lander's passing ability and stability in complex terrains. Moreover, this work considers the longitudinal stability margin (LSM) method and minimum stability margin of the lander as a sequential optimization problem. Hence, the hierarchical control architecture is established to compensate for the mission and environment changes, improving computational efficiency. Finally, the developed method is applied to the simulation prototype to verify its performance in various environments. The experimental results demonstrate that the proposed method allows the WLL to move in various environments and improves its stability in simulation experiments. At the same time, compared with the foot endpoint trajectory gait control method, our method can improve the walking efficiency by 8.56% and 6.58%, respectively.

From Walking to Running: 3D Humanoid Gait Generation via MPC.

We present a real time algorithm for humanoid 3D walking and/or running based on a Model Predictive Control (MPC) approach. The objective is to generate a stable gait that replicates a footstep plan as closely as possible, that is, a sequence of candidate footstep positions and orientations with associated timings. For each footstep, the plan also specifies an associated reference height for the Center of Mass (CoM) and whether the robot should reach the footstep by walking or running. The scheme makes use of the Variable-Height Inverted Pendulum (VH-IP) as a prediction model, generating in real time both a CoM trajectory and adapted footsteps. The VH-IP model relates the position of the CoM to that of the Zero Moment Point (ZMP); to avoid falling, the ZMP must be inside a properly defined support region (a 3D extension of the 2D support polygon) whenever the robot is in contact with the ground. The nonlinearity of the VH-IP is handled by splitting the gait generation into two consecutive stages, both requiring to solve a quadratic program. Thanks to a particular triangular structure of the VH-IP dynamics, the first stage deals with the vertical dynamics using the Ground Reaction Force (GRF) as a decision variable. Using the prediction given by the first stage, the horizontal dynamics become linear time-varying. During the flight phases, the VH-IP collapses to a free-falling mass model. The proposed formulation incorporates constraints in order to maintain physically meaningful values of the GRF, keep the ZMP in the support region during contact phases, and ensure that the adapted footsteps are kinematically realizable. Most importantly, a stability constraint is enforced on the time-varying horizontal dynamics to guarantee a bounded evolution of the CoM with respect to the ZMP. Furthermore, we show how to extend the technique in order to perform running on tilted surfaces. We also describe a simple technique that receives input high-level velocity commands and generates a footstep plan in the form required by the proposed MPC scheme. The algorithm is validated via dynamic simulations on the full-scale humanoid robot HRP-4, as well as experiments on the small-sized robot OP3.

Zero Moment Line-Universal Stability Parameter for Multi-Contact Systems in Three Dimensions.

The widely used stability parameter, the zero moment point (ZMP), which is usually defined on the ground, is redefined, in this paper, in two different ways to acquire a more general form that allows its application to systems that are not supported only on the ground, and therefore, their support polygon does not extend only on the floor. This way it allows to determine the stability of humanoid and other floating-based robots that are interacting with the environment at arbitrary heights. In the first redefinition, the ZMP is represented as a line containing all possible ZMPs, called the zero moment line (ZML), while in the second redefinition, the ZMP is represented as the ZMP angle, i.e., the angle between the ZML and the vertical line, passing through the center of mass (COM) of the investigated system. The first redefinition is useful in situations when the external forces and their acting locations are known, while the second redefinition can be applied in situations when the COM of the system under study is known and can be tracked. The first redefinition of the ZMP is also applied to two different measurements performed with two force plates, two force sensors, and the Optitrack system. In the first measurement, a subject stands up from a bench and sits down while being pulled by its hands, while in the second measurement, two subjects stand still, hold on to two double handles, and lean backward. In both cases, the stability of the subjects involved in the measurements is investigated and discussed.

Polygon-Based Random Tree Search Algorithm for a Size-Changing Robot

This paper proposes the Polygon-based Random Tree search algorithm with Variable polygon size (PRT-V) for Variable Topology Truss (VTT). This algorithm improves on our previous path planning algorithm by using VTTs ability to change its size drastically. The algorithm assigns stopover points at the key locations in environments between the initial and goal points. Stopover points are used as reference points for both path planning and size adjustment. A Voronoi diagram-based roadmap method is used to automatically find appropriate stopover points. Based on the stopover points, the desired support polygons and the corresponding nominal lengths are generated by PRT-V. Then, the locomotion of VTT is generated by a non-impact locomotion algorithm to prevent tipping over. Simulations verify the performance of PRT-V in three different workspaces with obstacles. With PRT-V, VTT can squeeze through narrow passages or move efficiently in large spaces by increasing size, a unique feature.

Https://www.ijraset.com/best-journal/system-based-application-for-reading-and-learning-ayurveda-sutras

Abstract: The rocker- dread suspense system has robust capabilities to deal with uneven terrain because of its distributing of the cargo over its six bus slightly, while there's one major failing to high- speed traversal over the planar terrain. This paper proposes a new dynamic rocker- dread suspense system with two modes of operation it can expand the span of the rocker- dread support polygon to increase trip rate when the terrain is planar; and it can switch to its original configuration to move in low speed when it's faced with rough terrain. The analysis on dynamic stability periphery and kinematical simulation on the two operating modes of rocker- dread are employed to dissect and corroborate the rationality and effectiveness of the revision in the structure.

Towards Terrain Adaptablity: In Situ Transformation of Wheel-Biped Robots

Most existing bipedal robots can only move with either their wheels or feet. Even if some of them are capable of transforming between these two motions, they need to change their configuration dramatically. In order to truly combine the advantages of wheeled and footed robots, in this letter, an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> transformation method is investigated and implemented on a wheel-biped transformable robot <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SR600-II</i> . <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">In situ</i> transformation means a transforming process with minimum position and configuration changes. It includes two processes: foot-to-wheel (FtW) and wheel-to-foot (WtF) transformations, both of which have to pass by transition states (termed critical states) that both foot and wheel contact with floor. At critical states, the robot has to meet both constraints of wheeled and footed balances. For footed balance, the center of mass (CoM) needs to fall within the support polygon formed by the feet. In order to maintain <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> wheeled balance, the upper body posture needs to be adjusted in real-time during the transformation process to make the vertical projection of the CoM be kept between the two wheels. To achieve a smooth transformation and minimize changes in robot joints, a projection-based algorithm is proposed to adjust the robot posture to comply with both constraints. Simulations and experiments on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SR600-II</i> prototype have validated the effectiveness of the proposed design and control strategy for wheel-biped transformable robots.

Adaptive Interlimb Coordination Mechanism for Hexapod Locomotion Based on Active Load Sensing.

Insects can flexibly coordinate their limbs to adapt to various locomotor conditions, e.g., complex environments, changes in locomotion speed, and leg amputation. An interesting aspect of insect locomotion is that the gait patterns are not necessarily stereotypical but are often highly variable, e.g., searching behavior to obtain stable footholds in complex environments. Several previous studies have focused on the mechanism for the emergence of variable limb coordination patterns. However, the proposed mechanisms are complicated and the essential mechanism underlying insect locomotion remains elusive. To address this issue, we proposed a simple mathematical model for the mechanism of variable interlimb coordination in insect locomotion. The key idea of the proposed model is “decentralized active load sensing,” wherein each limb actively moves and detects the reaction force from the ground to judge whether it plays a pivotal role in maintaining the steady support polygon. Based on active load sensing, each limb stays in the stance phase when the limb is necessary for body support. To evaluate the proposed model, we conducted simulation experiments using a hexapod robot. The results showed that the proposed simple mechanism allows the hexapod robot to exhibit typical gait patterns in response to the locomotion speed. Furthermore, the proposed mechanism improves the adaptability of the hexapod robot for leg amputations and lack of footholds by changing each limb's walking and searching behavior in a decentralized manner based on the physical interaction between the body and the environment.

Development of a Wearable Chair

We have developed wearable chairs for various people. If an elderly person gets tired while walking, he/she can sit down and take a rest at any time, so that he or she can expand their range of motion. If a worker has to work in a crouching posture for a long time, using this device can reduce the burden on the body. This device is designed so that it can be stored as small as possible, and at the time of sitting, the support polygon is as large as possible, and the center of gravity is at the center. The muscle activity of the thigh was measured by changing the height of this chair. As a result, it was found that the lower the chair, the lower the muscle activity when sitting down, but the higher the chair, the lower the muscle activity when standing up, and the easier it is to stand up.

Biomechanical variables affect peri-implant bone loss in implant-supported fixed complete dentures: A methodological and prospective study.

Implant-supported fixed complete dentures (IFCD) experience failures and complications related to biological and technical risk factors. This study investigated the effect of biomechanical variables of IFCD on 1-year peri-implant bone loss at the buccal, palatal/lingual, mesial, and distal implant sides. A new method was used to measure the geometric biomechanical variables of IFCD using cone beam computed tomography (CBCT). The study sample consisted of 246 external hexagon implants supporting 48 hybrid IFCD in 44 patients. CBCT images obtained immediately (T0) and 1 year (T1) after prosthesis installation were used to measure the support polygon area, clinical crown/implant (C/I) ratio (vertical lever), anteroposterior power and resistance arms, anterior and posterior cantilevers (horizontal levers), and peri-implant bone remodeling (T1-T0). Data were analyzed using multilevel multivariable models. The average total bone loss in the mandible and maxilla were 0.88 mm, with a loss of 0.62 mm in the mandible and 1.08 mm in the maxilla. The C/I ratio had a significant effect on bone loss on the mesial, distal, and palatal/lingual sides (P <.05). The anterior cantilever had a protective effect on the lingual side of the anterior implant. No effect on bone loss was found for the support polygon area, posterior cantilever, resistance arm, or power arm (P >.05). The results suggest that the C/I ratio and anterior cantilever in IFCD affect peri-implant bone loss according to the implant side and position in the arch.

Development of an Agile Omnidirectional Mobile Robot With GRF Compensated Wheel-leg Mechanisms for Human Environments

Wheeled mobile robots have been receiving continuous attention in various fields because of their stability, efficiency, and simple mechanisms. However, most of them require significantly larger occupied space than humans and have limited maneuverability in the environment for humans, such as crowded corridors, floor thresholds, ramps, and elevators. This letter presents a new wheel-leg mobile robot that combines the legs for changeable support polygon and mecanum wheels for holonomic motion. The robot has a human-like slim shape with 4 wheel-leg mechanisms, each of which has one 2-DOF leg frame and one mecanum wheel. To allow 2-DOF leg motion while maintaining the orientation of the mecanum wheels, a unique parallel link mechanism was devised. In order to achieve agile motion and impact and vibration absorption capability, a back-drivable high payload compound planetary gear was developed. The ground reaction force (GRF) compensation mechanism in each leg reduces the required payload of the actuators. The letter describes the detailed mechanical design of the robot and the actuators. The effectiveness of the proposed robot was verified in various experiments, fast omnidirectional motion test, a climbing test of a single step, and a motion test in the elevator with people.