The ability of quadruped robots to overcome obstacles is a critical factor that limits their practical application. Here, a design concept and a control algorithm are presented that aim at enhancing the explosive force of quadruped robots during jumping by utilizing elastic energy storage components. The hind legs of the quadruped robot are designed as energy storage units. Tension springs are utilized as components for storing energy and are installed in a parallel structure on the hind leg. Energy is stored during the compression process of the robot’s torso and released during the jumping phase. The optimal foot force is calculated using a single rigid body model. The mapping relationship between the force applied to the foot and the resulting joint torque is established by developing a dynamic model of the hind legs. Simulation experiments were conducted using the Webots physics engine to compare the impact of varying spring stiffness on joint torque during the jumping process. This study determined the optimal spring stiffness under specific conditions. The hind legs’ torque saving ratio reaches 19%, and the energy-saving ratio reaches 13%, which validates the effectiveness and feasibility of integrating elastic energy storage components.

Evolution has shown that legged locomotion is most adequate for tasks requiring versatile movement on land, allowing animals to traverse a wide variety of environments ranging from natural terrain to artificial, man-made landscapes with great ease. By employing well-designed control schemes, this ability could be replicated for legged robots, enabling them to be used in critical situations that still pose great danger to human integrity, such as search and rescue missions, inspection of hazardous areas, and even space exploration. This work characterizes the quadruped robot and contact dynamics that will compose our in-house simulator to be used for prototyping locomotion control schemes applied to quadruped robots. The proposed simulator computes the robot dynamics using the Recursive Newton-Euler and Composite-Rigid-Body algorithms with a few modifications to make certain aspects relevant for contact detection and control more easily accessible; furthermore, a compliant contact force method alongside stick-slip friction modeled the contact dynamics. To allow the robot to move, a simple PD-independent joint controller was implemented to track a desired leg trajectory. With the same robot and controller implemented using the MuJoCo simulation software, this work evaluates the proposed simulator by comparing characteristic locomotion signals such as the trunk pose and the ground reaction forces. Results showed similar behavior for both simulators, especially with regard to the contact detection, despite the significantly different contact models. Lastly, final remarks to enhance our simulator’s performance are suggested to be explored in future works.

Real-time gait trajectory planning is challenging for legged robots walking on unknown terrain. In this paper, to realize a more efficient and faster motion control of a quadrupedal robot, we propose an optimized gait planning generator (GPG) based on the decision tree (DT) and random forest (RF) model of the robot leg workspace. First, the framework of this embedded GPG and some of the modules associated with it are illustrated. Aiming at the leg workspace model described by DT and RF used in GPG, this paper introduces in detail how to collect the original data needed for training the model and puts forward an Interpolation Labeling with Dilation and Erosion (ILDE) data processing algorithm. After the DT and RF models are trained, we preliminarily evaluate their performance. We then present how these models can be used to predict the location relation between a spatial point and the leg workspace based on its distributional features. The DT model takes only 0.00011 s to process a sample, while the RF model can give the prediction probability. As a complement, the PID inverse kinematic model used in GPG is also mentioned. Finally, the optimized GPG is tested during a real-time single-leg trajectory planning experiment and an unknown terrain recognition simulation of a virtual quadrupedal robot. According to the test results, the GPG shows a remarkable rapidity for processing large-scale data in the gait trajectory planning tasks, and the results can prove it has an application value for quadruped robot control.

This paper proposes a robot model with multiple spines and investigates its effects on the bounding gait of quadruped robot. Contrastive tests, carried out by adding an active driving joint (ADJ) and changing the number of passive driving joints, were divided between simulation and physical. The results reveal that the spinal structure (one ADJ and several passive driving joints) is closely related to the performance parameters. Increasing the number of passive driving joints can improve the velocity and energy efficiency. This structure may have significant guidance for designing a quadruped robot.

Currently, the body balance control algorithm of a quadruped robot executing trot gait motion is more complex and computationally intensive, which is not conducive to improving the real-time control performance of the robot. This paper proposes a six-dimensional spatial mechanics decoupling algorithm to enhance the balance control accuracy during trot gait while optimizing the computational effort. A 6 × 6 matrix is established to describe the relationship between six ground reaction forces of the diagonal supporting leg and six spatial forces and torques controlling robot degrees of freedom, which is optimized to reach the full rank. Decoupling calculation is adopted to obtain required ground reaction forces by matrix inverse operation, and forces are converted to joint motor torques utilizing the Jacobian matrix. The trajectory of the swing leg foot is generated based on cubic interpolation, and the robot motion speed is adjusted by selecting the landing point. This paper also proposes a region intervention control method based on center of mass projection to regulate the moving speed while ensuring the balance of the robot. Finally, the algorithm is verified by simulation using open source software Webots. The results show that when the robot moves at an average speed of 0.5 m/s, the lateral displacement change of the robot is less than 0.009 m, the height change is less than 0.003 m, and the rotating angles around the x, y, and z axes are less than 0.0036 rad, 0.0013 rad, and 0.001 rad, respectively.

A kinetostatic approach applied to the design of a backflip strategy for quadruped robots is proposed in this paper. Inspired by legged animals and taking the advantage of the leg workspace, this strategy provides an optimal design idea for the low-cost quadruped robots to achieve self-recovery after overturning. Through kinetostatic and energy analysis, a four-stepped backflip strategy based on the selected rotation axis with minimum energy is proposed, with a process of selection, lifting, rotating, and protection. The kinematic factors that affect the backflip are investigated, along with the relationship between the design parameters of the leg and trunk being analyzed. At the end of this paper, the strategy is validated by a simulation and experiments with a prototype called DRbot, demonstrating that the strategy endows the robot a strong self-recovery ability in various terrains.

This paper presents the detailed dynamic modeling of a quadruped robot. The forward and inverse kinematic analysis of each leg of the proposed model is deduced using Denavit-Hartenberg (D-H) parameters. It desires to calculate the optimal feet forces of the quadruped robot’s joint torque, which is essential for its online control. To find out the optimal feet force distribution, two approaches are implemented to fulfill the locomotion objective. The four-legged quadruped robot and torso body’s detailed dynamics are modeled to generate an equation of motion for the robot control system. The Euler–Langrage theory has been used to find out the joint motion. The computer simulation results are presented to verify the effectiveness of the dynamic model.

We designed a quadruped robot with a one-degree-of-freedom (1-DOF)-pitch head, a 1-DOF-roll tail, and 14 active DOFs in total, which are controlled via a central pattern generator (CPG) based on a Hopf oscillator. Head and tail movements are coupled to the leg movements with fixed phase differences. Experiments show that tail swinging in roll can equilibrate feet–ground reaction forces (GRF), reducing yaw errors and enabling the robot to maintain its direction when trotting. Head swing in pitch has the potential to increase flight time and stride length of the swinging legs and increase the robot's forward velocity when running in bounds.

Legged robots have the potential to navigate in more challenging terrains than wheeled robots. Unfortunately, their control is more demanding, because they have to deal with the common tasks of mapping and path planning as well as more specific issues of legged locomotion, like balancing and foothold planning. In this paper, we present the integration and the development of a stabilized vision system on the fully torque-controlled hydraulically actuated quadruped robot (HyQ). The active head added onto the robot is composed of a fast pan and tilt unit (PTU) and a high-resolution wide angle stereo camera. The PTU enables camera gaze shifting to a specific area in the environment (both to extend and refine the map) or to track an object while navigating. Moreover, as the quadruped locomotion induces strong regular vibrations, impacts or slippages on rough terrain, we took advantage of the PTU to mechanically compensate for the robot's motions. In this paper, we demonstrate the influence of legged locomotion on the quality of the visual data stream by providing a detailed study of HyQ's motions, which are compared against a rough terrain wheeled robot of the same size. Our proposed Inertial Measurement Unit (IMU)-based controller allows us to decouple the camera from the robot motions. We show through experiments that, by stabilizing the image feedback, we can improve the onboard vision-based processes of tracking and mapping. In particular, during the outdoor tests on the quadruped robot, the use of our camera stabilization system improved the accuracy on the 3D maps by 25%, with a decrease of 50% of mapping failures.

In this paper, a model-based exponential stabilization of a quadruped robot is studied in bounding motion. The dynamics of the five-link planar underactuated mechanical model of the quadruped robot with four actuated joints system is derived. It is shown that the dynamical equation of the proposed simplified model belongs to a class of second-order nonholonomic mechanical systems which cannot be stabilized by any smooth time-invariant state feedback. Utilizing a coordinate transformation based on the so-called normalized momentum, a robust backstepping control method is presented for the quadruped robot. Both theoretical analysis and numerical simulations show that the robust backstepping controller can stabilize the underactuated quadruped robot so that it could balance on its rear legs and track a desired trajectory. Despite the model parameter uncertainties, the robustness of the controller is maintained. The simulation results show the effectiveness of the proposed method.

A method of planning crab gaits for a quadruped walking robot is proposed. In the conventional gait study, one of the major concerns has been the foothold selection based on a prescribed body motion, but, in the paper, we consider the body motion planning problem under the assumption that a set of irregular footholds is given, and propose a hierarchical strategy. The strategy can be divided into three stages: first, a feasible range of the body movement is sought under the kinematic limit and the stability constraint. Next, a swing-leg sequence is selected with the aid of a proposed measure of traversability. Finally, an optimal sequence of the body motion is planned by the proposed procedure of otpimizing the gait stability margin. To verify the efficiency of the proposed method, simulation results are presented.

The description is provided for the design and implementation of a system capable of simulating the motions of a quadruped walking robot. The system aims to investigate the feasibility of the robot's walking cycle. This is achieved by considering the robot's stability and more specifically the position of its centre of gravity in relation to its supporting legs. The robot is modelled as a solid body connected to four jointed limbs which are moved through a series of gaits, their positions being calculated at a set of discrete intervals. The resulting information is displayed using a graphical module to present an image of the moving robot and indicate its centre of gravity and support pattern. The complete system indicates the stability of the robot throughout a user-defined gait cycle and is both portable and adaptable.

The system is implemented on a HLH Orion and an Atari 1040ST in the C programming language and is aimed at providing support for the Department of Mechanical Engineering at Edinburgh University where the particular robot is being built.

A multifunctional 4 legged walking machine that is being developed in the Robotics Research Centre (NTU) is described. The major factors influencing the design requirements include minimisation of the weight of the machine and maximisation of workspace of the legs. The designed walking machine can adopt a variety of configurations, such as insect, mammalian, reptile or human. The device is invertable (i.e. can turn over). It can use its legs as manipulators, hence it can perform basic pick-and-place functions. A control system was built using the QNX real-time operating system platform. The software was designed using the client-server approach.