Hierarchical control framework for multi-legged extraterrestrial exploration robot based on model predictive and virtual model control

As for a motion control framework of robots, virtual model control (VMC) can use virtual components to create virtual forces/torques. Actually, the virtual forces/torques are generated by joint actuators when the virtual components interact between robots and environments. In this paper, a virtual model control is proposed to do the dynamic balance control of quadruped robots in trot gait. In each leg, virtual model control includes swing phase control of robots and stance phase counterparts. In whole body, based on the forces/torques distribution method between two stance legs, virtual model control is mainly about the attitude control containing roll, pitch and yaw. Then, an intuitive approach of velocity control is employed for the locomotion of quadruped robots. Based on the velocity planning and control, a trajectory tracking control approach is investigated by considering four factors: terrain complexity index, curvature radius of given trajectory, distance to terminal, and maximum velocity of quadruped robots. Finally, the effectiveness of proposed controllers is validated by co-simulations.

The transformation from high level task specification to low level motion control is a fundamental issue in sensorimotor control in animals and robots. This paper describes a control scheme called virtual model control that addresses this issue. Virtual model control is a motion control language that uses simulations of imagined mechanical components to create forces, which are applied through real joint torques, thereby creating the illusion that the virtual components are connected to the robot. Due to the intuitive nature of this technique, designing a virtual model controller requires the same skills as designing the mechanism itself. A high level control system can be cascaded with the low level virtual model controller to modulate the parameters of the virtual mechanisms. Discrete commands from the high level controller would then result in fluid motion. Virtual model control has been applied to a physical bipedal walking robot. A simple algorithm utilizing a simple set of virtual components has successfully compelled the robot to walk continuously over level terrain.

This article presents an intuitive approach based on virtual model control for quadrupedal dynamic locomotion, aiming at simple and robust trotting control. The controller consists of two main modules: stance phase virtual model control for full control of the robot body and swing phase virtual model control for control of swing legs. We combine the decomposed virtual model control with Raibert’s method to intuitively regulate the height, speeds and attitude of the body during stance phase, with special attention to the rotation about the body diagonal line. To unify the control law and further simplify the controller, virtual model control is also implemented for swing legs to follow the planned swing foot trajectories that are self-adapting depending on the speeds of the robot. Simulations including forward trotting, lateral push recover, and lateral travel are presented to demonstrate the effectiveness and robustness of our controller.

Virtual model control is a motion control framework that uses virtual components to create virtual forces/torques, which are actually generated by joint actuators when the virtual components interact with robot systems. Firstly, this paper employs virtual model control to do a dynamic balance control of whole body of quadruped robots' trot gait in a bottom controller. In each leg, there exists a designed swing phase virtual model control and a stance phase counterparts. In the whole body, virtual model control is utilized to achieve a attitude control containing roll, pitch and yaw. In the attitude control, a forces/torques distribution method between two stance legs is pre-investigated. In a high-level implemented controller, an intuitive velocity control approach proposed by Raibert is applied for the locomotion of quadruped robots. Secondly, an anti-disturbance control, which contains compensating gravity, adjusting step length, adjusting swing trajectory, adjusting attitude, and adjusting virtual forces/torques, is investigated to improve the robustness, terrain adaptability, and dynamic balance performance of quadrupedal locomotion. Thirdly, a trajectory tracking control method based on an intuitive velocity control is addressed through considering four factors: terrain complexity index, curvature radius of given trajectory, distance to terminal, and maximum velocity of quadruped robots. Finally, simulations validate the effectiveness of proposed controllers.

Most of control strategies are based on complex mathematical equations and the success of them is directly related to the precise acquisition of the mathematical model of the system. Virtual Model Control (VMC) allows the system to be mechanically controlled like a puppet with intuitive approaches instead of complex mathematical equations. In this paper, a novel implementation of fuzzy VMC on inverted pendulum, which is an under actuated mechanism, is presented. The cart of the inverted pendulum is controlled by manipulating the vertical equilibrium point of the pendulum with two cascaded VMCs. A Takagi-Sugeno fuzzy parameter tuner is designed to improve the VMC performance. An LQR controller is also designed to compare the performances of the controllers. The complete control system is implemented on FPGA based embedded platform in real time. The simulation and experimental results indicated that the proposed VMC successfully controls the inverted pendulum. In addition, the VMC with fuzzy parameter tuner has lower rise time, settling time, IAE and ITAE when compared to the LQR which is widely used controller in the literature.

In this paper, Virtual Model Control (VMC) is proposed to address the gait control problem of a space hexapod robot. In the VMC framework, a series of virtual elements, like springs and dampers, are attached to specific points on the body to generate desired joint torques. Especially, the control of the gait is divided into two phases: stance phase and swing phase. In the former, the VMC is exploited to compute the torques for the standing legs required to control the body height and attitude. The virtual elements are attached to the hips in such a way to govern each degree of freedom. On the other hand, in the latter phase, the VMC provides the control actions for the swing legs to follow a desired trajectory. In this case, the springs and dampers are attached between the foot of the leg and a point on the desired trajectory. The legs alternate these two modes cyclically and this switch is commanded by a state machine. In this work, three possible gaits are considered: tripod gait, wave gait and stick gait. The strength of the VMC and its suitability for space applications lie on its intuitiveness, robustness and computational efficiency. The effectiveness and performance of the proposed approach are assessed through numerical simulations considering different terrain roughness.

The virtual model control (VMC) method establishes a direct correlation model between the end-effector and the main body by selecting appropriate virtual mechanical components. This approach facilitates direct force control while circumventing the necessity for complex dynamic modeling. However, the simplification inherent in this modeling can result in inaccuracies in the calculation of joint driving torques, ultimately diminishing control precision. Moreover, VMC typically depends on predefined models for control, which constrains its adaptability in dynamically complex environments and under varying movement conditions. To address these limitations, this paper proposes the BP-VMC method, which is based on a backpropagation neural network (BPNN). Initially, a quadruped robot model was established through kinematic analysis. Subsequently, a decomposed VMC model was developed, and BPNN was introduced to facilitate the adaptive tuning of virtual parameters. This approach resulted in the creation of a virtual mechanical component model with adaptive capabilities, compensating for errors arising from simplified modeling. Finally, a simulation control system was constructed based on the BP-VMC control framework to validate the optimization of control performance. Simulation experiments demonstrated that, in comparison to traditional VMC methods, the BP-VMC method exhibits enhanced control accuracy and stability, achieving a 30% reduction in trajectory tracking error, a 40% reduction in velocity tracking error, and a 20–30% improvement in instability indices across various working conditions. This evidence underscores the BP-VMC method’s robust adaptability in dynamic environments.

Design of trot gait parameters planning system for parallel quadruped robot based on virtual model controller and fuzzy neural network.

Virtual model control (VMC) is the most widely-used method for motion control of quadruped robot. VMC could decrease the abrupt ground reaction force and realize compliant interaction between foot and ground at the cost of control precision. To improve the robustness and precision of VMC, we integrate a fractional-order virtual damper with the classical VMC and propose a fractional-order VMC (FOVMC) for quadruped robot trotting motion. And we provide the implementation details about optimization-based FOVMC parameter tuning method and carry out the trotting experiments on the quadruped robot platform. The experiment results demonstrate that FOVMC could improve the precision of single-leg motion control and achieve a better whole-body trotting performance than classical VMC.

Quadruped robots have excellent application prospects whereas the locomotion control of them on rough terrains is still a challenging problem, especially for those of large scales. The existing methods are either too complicated or lack of accuracies due to assumptions used. This paper presents a novel control algorithm for quadruped robots running on rough terrains inspired by the virtual model control and the model predictive control. State recursions are carried out based on the dynamic model of the trunk during the standing phase. The modeling of the body is implemented in the self-defined motion reference frame that avoids global state estimations and accumulative errors. The force distribution of the standing legs is realized by quadratic optimization involving state predictions. Forces of the swing legs are calculated by the virtual spring-damping model that follow the desired trajectory which is robust to external disturbances. These two sub-controllers are combined by the time-force based state machine. Simulation results show that the quadruped robot obtains the adaptability to rough terrains and robustness to lateral pushes with the proposed method.

Model Predictive Control (MPC) of traditional Dual Three-phase Permanent Magnet Synchronous Motor (DTP-PMSM) algorithm often uses a single virtual vector to suppress harmonics, but its vector range is limited, resulting in a large ripple in torque and current in the control effect. Given the aforementioned issues, this study suggests a Double Virtual Vector Model Predictive Current Control (DVV-MPCC) strategy. Utilizing the foundation of the virtual vector, a zero vector and the adjacent virtual vector are combined to construct an anticipated voltage vector, so that the output range of the synthetic vector can reach any amplitude and direction. By incorporating the deadbeat concept, the calculation of the action time for each virtual vector is precisely determined. Finally, the prediction model is employed to refine the value function, enabling the selection of the optimal expected vector for implementation on the inverter. The simulation outcomes demonstrate the effectiveness of the strategy in mitigating torque ripple and current ripple.

This paper presents a hierarchical model predictive control (MPC) framework for hybrid power or propulsion systems that can be used in future energy-optimized aerospace systems. This control framework aims to decouple the slow energy optimization from dynamic power management in a holistic optimized manner and can be implemented on heterogeneous real-time computing hardware. The higher-level MPC minimizes the power generation costs and power delivery losses subject to dynamic load profiles, as well as maintains a dynamic level of reserved energy in energy storage to meet future changes in power demand. The lower-level MPC is to optimize the dynamic power management, i.e., controlling the currents to satisfy transient power flow needs while regulating the bus voltage. As such, the power generators should not necessarily meet the peak power demand, but just the average load demand. The proposed hierarchical MPC framework organically integrates energy optimization and dynamic power management in a decoupled manner and is suitable for integrated control of propulsion, power and thermal systems which are multi-input-multi-output control systems and very challenging with traditional PID-like approaches. This hierarchical MPC framework can perform multi-objective optimization and meet multiple constraints such as economic, operational, safety and power quality constraints at different levels. Challenges such as control objectives assignment, model selection, and constraint considerations are addressed in the paper. This framework can cover a wide bandwidth of model fidelity and enforce all necessary physical laws in the models using both MPCs together. State variable constraints are explicitly included in the controller formulation by using the equality constraints (i.e., discretized model or system state transfer equations) to transform the state constraints to the control constraints. The hierarchical MPC framework allows operational constraints to be assigned to different levels of MPC schemes. Simulation results show that the hierarchical control system operates well in optimizing for both energy flow and dynamic current/voltage regulations under dynamic conditions. By examining the interactions between two levels of MPC, it is shown that the objectives and constraints can be transferable but tradeoff should be made to achieve better coordination. This work will provide a capability of reconfigurable control paradigm on the same control platform via dynamic selection of control objectives and models.

Due to model predictive control can better deal with the constraints problem of nonlinear systems and improve the dynamic performance of the controlled system, therefore, this technology has attracted much attention in the field of motor drive. This article first introduced the basic principle of model predictive control, continuous control set model predictive control and finite control set model predictive control. Secondly, summarized the research status of generalized predictive control, explicit model predictive control, model predictive current control, model predictive torque control and commonly used improved model predictive control in motor drive systems. Thirdly, prospected the future development trend based on the current research status of model predictive control in motor drive system. Finally, the advantages and disadvantages of the continuous control set model predictive control and the finite control set model predictive control were comprehensively compared, and the ways in which the two algorithms act on the motor drive system were summarized.

Multi-vector model predictive control of permanent magnet synchronous motor can effectively overcome the shortcomings of conventional single-vector model predictive control such as large motor current ripples and limited control accuracy, but its control performance is more susceptible to the influence of motor parameter perturbation. To improve the robustness of the multi-vector predictive control algorithm under the motor parameter perturbation, a novel nonparametric three-vector model predictive current control method for permanent magnet synchronous motors is proposed in this paper. Through constructing an ultra-local predictive current model based on the input and output signals of the permanent magnet synchronous motor, the influence of motor parameter perturbation on current prediction is avoided, and a disturbance observer is designed to estimate the non-modeled and perturbed parts of the ultra-local model. In addition, the direct calculation method of vector duty cycles based on current error is introduced to suppress the influence of motor parameter uncertainty on the duty cycle calculation link, which further improves the system robustness. Finally, simulations and experiments of the proposed method are demonstrated to compare with the conventional parametric three-vector model predictive current control, and the results show that the proposed control strategy can effectively suppress the disturbances caused by the motor parameters and ensure the steady-state performance during motor operation.

The next generation of autonomous-legged robots will herald a new era in the fields of manufacturing, healthcare, terrain exploration, and surveillance. We can expect significant progress in a number of industries, including inspection, search and rescue, elderly care, workplace safety, and nuclear decommissioning. Advanced legged robots are built with a state-of-the-art architecture that makes use of stereo vision and inertial measurement data to navigate unfamiliar and challenging terrains. However, designing controllers for these robots is a difficult task due to a number of factors, including dynamic terrains, tracking delays, inaccurate 3D maps, unforeseen events, and sensor calibration issues. To address these challenges, this paper discusses the current methods for controlling autonomous-legged robots. Our primary contribution is comparative research on robot control strategies such as virtual model control (VMC), model predictive control (MPC), and model-free reinforcement learning (RL). This paper provides information on different strategies for controlling autonomous legged robots and discusses the potential advancements and applications of this technology in the future. The aim of this study is to assist future researchers in making informed decisions on the selection of optimal control strategies and innovative concepts when developing and working with legged robots.