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This article presents an intuitive approach based on virtual model control for robust quadrupedal trotting. The controller consists of two main modules: support phase virtual model control for torso motion control and flight phase virtual model control for flight toe trajectory generation. We mapped the relationship between the joint torques of sup...
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![Figure 3.3: The HyQ robot mapping the terrain using Octomap [35]. The...](profile/Carlos-Mastalli/publication/326201328/figure/fig5/AS:645001931390977@1530791852123/The-HyQ-robot-mapping-the-terrain-using-Octomap-35-The-voxel-map-is-generated-from_Q320.jpg)
Legged vehicles present a potential advantage over traditional wheeled systems since they offer greater mobility in rough and challenging terrain. However, most legged robots are still confined to structured and flat terrain. One of the main reasons for this is the difficulty in planning complex whole-body motions while taking into account future t...
The bipedal humanoid robot WABIAN-2R is developed to simulate human locomotion. Performing a walking motion requires a high torque at the ankle joint. WABIAN-2R consists of harmonic gears in its driveline system which increases the weight of each leg and respectively decreases the energy economy. However, using a spring mechanism instead of high ge...
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... Generally, the leg end of quadruped robots is spherical or arc-shaped, which can adapt to such minor attitude deviations. Therefore, the contact area between each leg end and the ground can be regarded as a point or small patch [15]. However, this study employs electromagnets as the adsorption structure, so the contact area between each leg end and the ferromagnetic plane is larger. ...
This paper aims to introduce robot technology to carry out the safety inspection of transmission towers in long-distance power transmission, so as to improve the safety and efficiency of inspection. However, aiming at the problem that the existing climbing robots are mainly used for large load applications, which leads to the large size and lack of flexibility of the robot, we propose an innovative solution. Firstly, a lightweight quadruped climbing robot is designed to improve portability and operational flexibility. Then, a one-dimensional force sensor is added at the end of each leg of the robot, and a special swing phase trajectory is designed. The robot can judge whether the electromagnetic adsorption is effective and avoid potential safety hazards. Finally, based on the principle of virtual model control (VMC), a foot-end force balancing algorithm is proposed to achieve uniform distribution and continuous change in force, and improve safety and load capacity. The experiments show that the scheme has a stable climbing ability in the environments of angle steel, vertical ferromagnetic plane and transmission tower.
... In order to fulfill the motion control of the quadruped robot, many models have been proposed, such as the zero moment point (ZMP) control [5], model predictive control (MPC) [6], virtual model control (VMC) [7], etc. Zhang et al. [8] calculated the optimal trajectory of the hip joint based on the stability margin of ZMP and used inverse kinematics principles to determine the robot joint angles. The feasibility of the method was verified on the BIT robot. ...
Animals have evolved to adapt to complex and uncertain environments, acquiring locomotion skills for diverse surroundings. To endow a robot’s animal-like locomotion ability, in this paper, we propose a learning algorithm for quadruped robots based on deep reinforcement learning (DRL) and a rhythm controller that is based on a cosine oscillator. For a quadruped robot, two cosine oscillators are utilized at the hip joint and the knee joint of one leg, respectively, and, finally, eight oscillators form the controller to realize the quadruped robot’s locomotion rhythm during moving. The coupling between the cosine oscillators of the rhythm controller is realized by the phase difference, which is simpler and easier to realize when dealing with the complex coupling relationship between different joints. DRL is used to help learn the controller parameters and, in the reward function design, we address the challenge of terrain adaptation without relying on the complex camera-based vision processing but based on the proprioceptive information, where a state estimator is introduced to achieve the robot’s posture and help finally utilize the food-end coordinate. Experiments are carried out in CoppeliaSim, and all of the flat, uphill and downhill conditions are considered. The results show that the robot can successfully accomplish all the above skills and, at the same time, with the reward function designed, the robot’s pitch angle, yaw angle and roll angle are very small, which means that the robot is relatively stable during walking. Then, the robot is transplanted to a new scene; the results show that although the environment is previously unencountered, the robot can still fulfill the task, which demonstrates the effectiveness and robustness of this proposed method.
... So far, there are mainly two ways to combine robust control for force control: robust impedance control and robust force-position hybrid control [153]. One-leg active compliance control was designed to establish a simplified mathematical model of the hydraulic driver [154]. The output torque of the robot joint was controlled using this model. ...
Motion control is crucial for multilegged robot locomotion and task completion. This study aims to address the fundamental challenges of inadequate foot tracking and weak leg compliance control in multilegged robot motions. The first section summarizes and discusses the feasibility and operability of smooth motion for multilegged robots based on the necessary conditions and application value of walking over complicated and unstructured terrain. The second to fourth sections present a qualitative research method of literature review to study the effects of several factors on the smooth motion of multilegged robots, including foot force perception and motion planning, active compliance control, gait stability, and Deep Reinforcement Learning (DRL) control. We conducted a case analysis of multilegged robots using traditional Nonlinear Model Predictive Control (NMPC), biomimetic Central Pattern Generator (CPG), and DRL control in the latest international open-source projects to help readers further follow the latest open-source algorithms for legged robot motion control. In addition, we analyze the challenges these influencing factors face in optimization and provide suggestions for effectively promoting the realization of review objectives. In the fifth section, we discuss the challenges of springy gait and intelligent switching control in solving the problems of poor foot tracking and weak leg compliance. We explore and forecast the potential application of the Probability Density Function (PDF) control of the foot force in the smooth motion of multilegged robots. In the sixth section, we systematically discuss, analyze, and summarize the existing problems in this research field. We also highlight the shortcomings of existing research methods, look forward to future research areas, and highlight the obstacles that need to be overcome to promote future research in this field.
... The HyQ robot developed by the Italian Institute of technology uses the virtual model of the leg to achieve better interaction with the ground [13,14]. Zhang et al. [15,16] proposed a trajectory tracking control method for quadruped robot diagonal trot gait based on a virtual model. This method sets up the support phase virtual model control and swing phase virtual model control, but only the static analysis of the system is carried out without considering the dynamics of the robot, which greatly simplifies the complexity of the model and leads to large errors in tracking control. ...
To improve the accuracy of tracking the trunk center-of-mass (CoM) trajectory and foot-end trajectory in a fully electrically driven quadruped robot, an efficient and practical new trajectory tracking control method is designed. The proposed trajectory tracking method is mainly divided into trunk balance controller (TBC) and swing leg controller (SLC). In TBC, a quadruped robot dynamics model is developed to find the optimal foot-end force that follows the trunk CoM trajectory based on the model predictive control (MPC) principle. In SLC, the Bessel curve is planned as the desired trajectory at the foot-end, while the desired trajectory is tracked by a virtual spring-damping element driving the foot-end, meanwhile, the radial basis function neural network (RBFNN) is applied for supervisory control to improve the control performance for the system. The experimental results show that the control method can modify the robot’s foot-end trajectory tracking effect, so that the stability error can be eliminated and the robustness of the controller can be improved, meanwhile, the linear and circular trajectory for CoM can be tracked accurately and quickly.
... m, I g and g are the robot's mass, centroidal rotational inertia and gravity vector. A virtual model [24][25][26] applied to the center can be employed to track the reference trajectory [14] by the PD controller as follows: ...
Quadruped robots are likely to fall into the fault joint state in outdoor explorations. The unexpected joint lock may suddenly happen when quadruped robots are implementing normal gaits, and maintaining the primal movement patterns to finish targeted tasks could be disastrous. In this paper, a fault-tolerant motion planning and generation method for quadruped robots with joint lock is proposed. Fault-tolerant cases on three types of joints on legs are investigated, and equivalent geometric models are proposed to reconstruct kinematics. To make unnecessary deformation of gait patterns as small as possible, the body posture and standing height of quadruped robots are to be optimized based on the nonlinear equivalent geometry models with constraints. The proposed fault-tolerant method is applicable to constructing a quasi-static whole-body controller, and it does not require additional operations and constraints of the fault leg. To validate the consistency and stability of the proposed fault-tolerant method, the experiments are implemented on the three joint lock failure scenarios for quadruped robots.
... The neural network control method based on the response and reflection mechanism of central pattern generator (CPG) is also widely used control method of quadruped robots [4]. The control method based on virtual model (VMC) firstly assumes the existence of virtual components on the control object, such as spring and damper, then analyzes the virtual force on the control object, and establishes the mapping relationship between virtual force and joint force through Jacobian matrix [5][6][7]. Handling the contact forces between the robot and the ground and reasonably distributing the joint forces is the basis for realizing the flexible and efficient movement of quadruped robot. HyQ [8][9] quadruped robot of IIT and StarlETH [10] quadruped robot of Zurich University of technology used VMC to achieve better plantar interaction and compliance characteristics. ...
In order to improve the dynamic walking performance of quadruped robot, a control method of optimizing feet forces distribution based on virtual model is proposed. In the supporting phase, the virtual model control method is applied to solve the virtual force of the torso. Combined with the gravity of the center of mass (CoM), the distribution problem between the virtual force of the CoM and the feet forces of the supporting legs is transformed into a quadratic programming (QP) problem, which is solved by Gurobi to realize the optimal distribution of the feet forces. Similarly, the virtual force of the swinging leg is solved by using the virtual model, and the joints torques of the robot’s swinging legs are obtained by combining the inverse dynamics feedforward of the swinging legs. Through the simulation of quadruped robot’s trot gait walking by webots and vs2019, it is verified that this method can stabilize the robot’s attitude angles and body speeds near the target values. Compared with the feet forces distribution method that abandons the lateral force control, the application of this method makes the fluctuation range of the attitude angles of the robot and the ground reaction forces (GRFs) of the supporting legs smaller. It is proved that this control method can effectively improve the walking stability and robustness of the quadruped robot.
... The staircase-climbing capability is essential for legged robots. Several legged robots have been reported to traverse the staircase successfully: the biped robots named Cassie [3] and ASIMO [4] , the quadruped robots named HyQ [5] , Anymal [6] , MIT Cheetah [7] , Pegasus [8] , Jueying [9] , Scalf [10] , THU-QUAD II [11] and ALPHRED [12] , the hexapod robot named Qingzhui [13] , P-H [14] , and Octopus [15] , and the legged robots in DARPA Robotics Challenge (DRC) [16] . ...
Robot dimension design based on staircase-climbing is essential but seldom studied for legged robots. Incorporating the staircase-climbing in design is novel and relevant. The robot dimension, including the leg dimension and the body dimension, affects the staircase-climbing capability. This paper studies the dimension design for a novel hexapod robot. In dimension design for the leg mechanisms, the critical problem is to handle the interferences between the leg mechanism and staircase. Firstly, all interferences in climbing a staircase are classified into three cases. The corresponding three conditions to avoid the three interference cases are originally proposed. Secondly, the dimension of a single leg mechanism is derived analytically according to the staircase size under the premise of avoiding the three interference cases. The robot body coordinates the leg mechanisms and affects the ability to adjust the tilting angle in climbing a staircase. The body dimension is derived analytically with the constraints of leg workspace, leg-staircase interferences, and the static stability margin. The design example of a hexapod robot climbing 35-degree and 45-degree staircases is given and verified by simulations and experiments.
... Other studies are expressly interested in the construction of low dimensional models of complex motion [11][12][13][14]. Still others are dedicated to finding how qualitative understandings of animal motion can be used to build robots that emulate some observed motion [15][16][17][18][19][20], with a notable emphasis on locomotion in quadrupeds [21][22][23][24][25][26][27] and bipeds [28][29][30][31][32][33]. ...
This paper describes the formulation and experimental testing of an estimation of submanifold models of animal motion. It is assumed that the animal motion is supported on a configuration manifold, Q, and that the manifold is homeomorphic to a known smooth, Riemannian manifold, S. Estimation of the configuration submanifold is achieved by finding an unknown mapping, γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}, from S to Q. The overall problem is cast as a distribution-free learning problem over the manifold of measurements. This paper defines sufficient conditions that show that the rates of convergence in Lμ2(S)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2_\mu (S)$$\end{document} of approximations of γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} correspond to those known for classical distribution-free learning theory over Euclidean space. This paper concludes with a study and discussion of the performance of the proposed method using samples from recent reptile motion studies.
... Similarly, in [9], the Minitaur quadruped robot, which uses a parallel-elastic leg mechanism, can bound up stairs with 19.6cm height just like a frog. Recently, the trot gait has been applied to several versatile quadruped robots, including Spot [10], MIT Cheetah [11], and SCalf [12], all showing success for the stair-climbing tasks. Among them, Spot has shown very impressive performance in climbing stairs with autonomous navigation, while MIT Cheetah is able to blindly climb stairs covered in debris through model predictive control and a contact detection algorithm. ...
An optimized static gait that combines pose optimization, motion sequence optimization, and a novel high-level planning algorithm is proposed for quadruped robots to walk on stairs. Firstly, an optimized pose is determined for the robot to stand on stairs statically. Then, a climbing gait cycle with an optimized motion sequence is presented, which takes the robot from one position and pose to another position and pose. Finally, a high-level planning algorithm is proposed to adjust the step length in each gait cycle to enable the robot to safely walk along the stairs. The proposed static gait maximizes the stair-climbing capability significantly while still guaranteeing walking safety, which provides a general solution for quadruped robots to walk on stairs of different sizes. Several simulations in V-REP are presented to evaluate the effectiveness of the optimized static gait generation technique in improving the stair-climbing capability. Compared to other quadruped robots developed recently, the robot tested in this paper can walk on a regular staircase with a rise of 20 cm and an inclination of 37.6°, and can also climb over a few steep narrow steps with a rise of 18 cm and a run of 5 cm.
... There are many models for legged-robot locomotion. Most researchers implement trajectory-based locomotion for its simplicity; this has been done in bipedal (Manchester et al., 2011)(Zhang et al., 2014b (Nandi et al., 2016) (Saputra et al., 2015a) (Khusainov et al., 2016) (Saputra et al., 2015c), quadrupedal (Winkler et al., 2015) (Kolter et al., 2008) (Mastalli et al., 2017) (Zhang et al., 2016) (Matsuzawa et al., 2016), and hexapodal robots (Qian and Goldman, 2015) (Zhu et al., 2016). Trajectory-based models control the motion planning in Cartesian coordinates using polynomial equations or Bézier curves (Manchester et al., 2011). ...
There are currently many quadruped robots suited to a wide range of applications, but traversing some terrains, such as vertical ladders, remains an open challenge. There is still a need to develop adaptive robots that can walk and climb efficiently. This paper presents an adaptive quadruped robot that, by mimicking feline structure, supports several novel capabilities. We design a novel paw structure and several point-cloud-based sensory structures incorporating a quad-composite time-of-flight sensor and a dual-laser range finder. The proposed robot is equipped with physical and cognitive capabilities which include: 1) a dynamic-density topological map building with attention model, 2) affordance perception using the topological map, and 3) a neural-based locomotion model. The novel capabilities show strong integration between locomotion and internal–external sensory information, enabling short-term adaptations in response to environmental changes. The robot performed well in several situations: walking on natural terrain, walking with a leg malfunction, avoiding a sudden obstacle, climbing a vertical ladder. Further, we consider current problems and future development.
