We present angle of attack control, a novel control strategy for a hip energized Penn Jerboa. The energetic losses from damping are counteracted by aligning most of the velocity at touchdown in the radial direction and the fore-aft velocity is controlled by using the hip torque to control to a target angular momentum. The control strategy results in highly asymmetric leg angle trajectories, thus avoiding the traction issues that plague hip actuated SLIP. Using a series of assumptions we find an analytical expression for the fixed points of an approximation to the hopping return map relating the design parameters to steady state gait performance. The hardware robot demonstrates stable locomotion with speeds ranging from 0.4 m/s to 2.5 m/s (2 leg lengths/s to 12.5 leg lengths/s) and heights ranging from 0.21 m to 0.27 m (1.05 leg lengths to 1.35 leg lengths). The performance of the empirical trials is well approximated by the analytical predictions.
This paper presents the design and validation of controlling hopping on the 3D bipedal robot Cassie. A spring-mass model is identified from the kinematics and compliance of the robot. The spring stiffness and damping are encapsulated by the leg length, thus actuating the leg length can create and control hopping behaviors. Trajectory optimization via direct collocation is performed on the spring-mass model to plan jumping and landing motions. The leg length trajectories are utilized as desired outputs to synthesize a control Lyapunov function based quadratic program (CLF-QP). Centroidal angula…
National Engineering School of Sfax, University of Sfax（斯法克斯大学斯法克斯国家工程学院）
In this paper the investigation is placed on the hierarchic neuro-fuzzy systems as a possible solution for biped control. An hierarchic controller for biped is presented, it includes several sub-controllers and the whole structure is generated using the adaptive Neuro-fuzzy method. The proposed hierarchic system focus on the key role that the centre of mass position plays in biped robotics, the system sub-controllers generate their outputs taken into consideration the position of that key point.
National Engineering School of Sfax, University of Sfax（斯法克斯大学斯法克斯国家工程学院）；Institute of Applied Sciences and technology of Sousse, University of Sousse（苏塞大学苏塞应用科学与技术研究所）
In this paper the design of a control system for a biped robot is described. Control is specified for a walk cycle of the robot. The implementation of the control system was done on Matlab Simulink. In this paper a hierarchical fuzzy logic controller (HFLC) is proposed to control a planar biped walk. The HFLC design is bio-inspired from human locomotion system. The proposed method is applied to control five links planar biped into free area and without obstacles.
We present a new walking controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of 3LP, the proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. The projection controller reacts to disturbances immediately and compared to the discrete LQR contr…
In this paper, disturbance reconstruction and robust trajectory tracking control of biped robots with hybrid dynamics in the port-Hamiltonian form is investigated. A new type of Hamiltonian function is introduced, which ensures the finite-time stability of the closed-loop system. The proposed control system consists of two loops: an inner and an outer loop. A fractional proportional-integral-derivative filter is used to achieve finite-time convergence for position tracking errors at the outer loop. A fractional-order sliding mode controller acts as a centralized controller at the inner-loop, e…
In this paper, a simple Neural controller has been used to achieve stable walking in a NAO biped robot, with 22 degrees of freedom that implemented in a virtual physics-based simulation environment of Robocup soccer simulation environment. The algorithm uses a Matsuoka base neural oscillator to generate control signal for the biped robot. To find the best angular trajectory and optimize network parameters, a new population-based search algorithm, called the Harmony Search (HS) algorithm, has been used. The algorithm conceptualized a group of musicians together trying to search for better state…
IEETA / DETI University of Aveiro（阿威罗大学 IEETA / DETI）
Generating robust locomotion for a humanoid robot in the presence of disturbances is difficult because of its high number of degrees of freedom and its unstable nature. In this paper, we used the concept of Divergent Component of Motion~(DCM) and propose an optimal closed-loop controller based on Linear-Quadratic-Gaussian to generate a robust and stable walking for humanoid robots. The biped robot dynamics has been approximated using the Linear Inverted Pendulum Model~(LIPM). Moreover, we propose a controller to adjust the landing location of the swing leg to increase the withstanding level of…
When legged robots impact their environment, they undergo large changes in their velocities in a small amount of time. Measuring and applying feedback to these velocities is challenging, and is further complicated due to uncertainty in the impact model and impact timing. This work proposes a general framework for adapting feedback control during impact by projecting the control objectives to a subspace that is invariant to the impact event. The resultant controller is robust to uncertainties in the impact event while maintaining maximum control authority over the impact invariant subspace. We …
Ohio State University（俄亥俄州立大学）；National Research Council of Canada（加拿大国家研究委员会）；University of Waterloo（滑铁卢大学）；Southern University of Science and Technology（南方科技大学）
This paper presents a neural-network based adaptive feedback control structure to regulate the velocity of 3D bipedal robots under dynamics uncertainties. Existing Hybrid Zero Dynamics (HZD)-based controllers regulate velocity through the implementation of heuristic regulators that do not consider model and environmental uncertainties, which may significantly affect the tracking performance of the controllers. In this paper, we address the uncertainties in the robot dynamics from the perspective of the reduced dimensional representation of virtual constraints and propose the integration of an …
Learning controllers for bipedal robots is a challenging problem, often requiring expert knowledge and extensive tuning of parameters that vary in different situations. Recently, deep reinforcement learning has shown promise at automatically learning controllers for complex systems in simulation. This has been followed by a push towards learning controllers that can be transferred between simulation and hardware, primarily with the use of domain randomization. However, domain randomization can make the problem of finding stable controllers even more challenging, especially for underactuated bi…
In this paper, previous works on the Model Predictive Control (MPC) and the Divergent Component of Motion (DCM) for bipedal walking control are extended. To this end, we employ a single MPC which uses a combination of Center of Pressure (CoP) manipulation, step adjustment, and Centroidal Moment Pivot (CMP) modulation to design a robust walking controller. Furthermore, we exploit the concept of time-varying DCM to generalize our walking controller for walking in uneven surfaces. Using our scheme, a general and robust walking controller is designed which can be implemented on robots with differe…
Robotics Institute, School of Computer Science, Carnegie Mellon University（卡内基梅隆大学计算机科学学院机器人研究所）；Robotics, Perception and Learning, CSC, KTH Royal Institute of Technology（瑞典皇家理工学院计算机科学与通信系机器人、感知与学习部门）
Controllers in robotics often consist of expert-designed heuristics, which can be hard to tune in higher dimensions. It is typical to use simulation to learn these parameters, but controllers learned in simulation often don't transfer to hardware. This necessitates optimization directly on hardware. However, collecting data on hardware can be expensive. This has led to a recent interest in adapting data-efficient learning techniques to robotics. One popular method is Bayesian Optimization (BO), a sample-efficient black-box optimization scheme, but its performance typically degrades in higher d…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Stanford University（斯坦福大学）
Whole-body control (WBC) is a generic task-oriented control method for feedback control of loco-manipulation behaviors in humanoid robots. The combination of WBC and model-based walking controllers has been widely utilized in various humanoid robots. However, to date, the WBC method has not been employed for unsupported passive-ankle dynamic locomotion. As such, in this paper, we devise a new WBC, dubbed whole-body locomotion controller (WBLC), that can achieve experimental dynamic walking on unsupported passive-ankle biped robots. A key aspect of WBLC is the relaxation of contact constraints …
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；University of Michigan（密歇根大学）；Ohio State University（俄亥俄州立大学）；Purdue University（普渡大学）
Controller design for bipedal walking on dynamic rigid surfaces (DRSes), which are rigid surfaces moving in the inertial frame (e.g., ships and airplanes), remains largely uninvestigated. This paper introduces a hierarchical control approach that achieves stable underactuated bipedal robot walking on a horizontally oscillating DRS. The highest layer of our approach is a real-time motion planner that generates desired global behaviors (i.e., the center of mass trajectories and footstep locations) by stabilizing a reduced-order robot model. One key novelty of this layer is the derivation of the …
We present a hierarchical whole-body controller leveraging the full rigid body dynamics of the wheeled bipedal robot Ascento. We derive closed-form expressions for the dynamics of its kinematic loops in a way that readily generalizes to more complex systems. The rolling constraint is incorporated using a compact analytic solution based on rotation matrices. The non-minimum phase balancing dynamics are accounted for by including a linear-quadratic regulator as a motion task. Robustness when driving curves is increased by regulating the lean angle as a function of the zero-moment point. The prop…
In the control of bipedal locomotion, linear velocity of the center of mass has been widely accepted as a primary variable for summarizing a robot's state vector. The ubiquitous massless-legged linear inverted pendulum (LIP) model is based on it. In this paper, we argue that angular momentum about the contact point has several properties that make it superior to linear velocity for feedback control. So as not to confuse the benefits of angular momentum with any other control design decisions, we first reformulate the standard LIP controller in terms of angular momentum. We then implement the r…
Korea Institute of Science and Technology（韩国科学技术研究院）；UNIVERSITY OF SCIENCE AND TECHNOLOGY（科学技术大学）
In this work, the hierarchical control strategy of template-based control for a bipedal robot is described. The axial force of a compliant leg is redirected to a point, called the virtual pivot point (VPP), of a 2D biped robot, which is located above the CoM of the model, to generate a restoring moment for the trunk motion. The resulting behavior of the model would resemble a virtual pendulum rotating around this VPP, thus aiming for an upright trunk during walking. Inspired by this analysis, we propose a new force redirecting method as a controller for robot walking. Then, these key features …
Keeping the stability can be counted as the essential ability of a humanoid robot to step out of the laboratory to work in our real environment. Since humanoid robots have similar kinematic to a human, humans expect these robots to be robustly capable of stabilizing even in a challenging situation like while a severe push is applied. This paper presents a robust walking framework which not only takes into account the traditional push recovery approaches (e.g., ankle, hip and step strategies) but also uses the concept of Divergent Component of the Motion (DCM) to adjust next step timing and loc…
The Cassie bipedal robot designed by Agility Robotics is providing academics a common platform for sharing and comparing algorithms for locomotion, perception, and navigation. This paper focuses on feedback control for standing and walking using the methods of virtual constraints and gait libraries. The designed controller was implemented six weeks after the robot arrived at the University of Michigan and allowed it to stand in place as well as walk over sidewalks, grass, snow, sand, and burning brush. The controller for standing also enables the robot to ride a Segway. A model of the Cassie r…
University of British Columbia（不列颠哥伦比亚大学）；Oregon State University（俄勒冈州立大学）
Bipedal locomotion skills are challenging to develop. Control strategies often use local linearization of the dynamics in conjunction with reduced-order abstractions to yield tractable solutions. In these model-based control strategies, the controller is often not fully aware of many details, including torque limits, joint limits, and other non-linearities that are necessarily excluded from the control computations for simplicity. Deep reinforcement learning (DRL) offers a promising model-free approach for controlling bipedal locomotion which can more fully exploit the dynamics. However, curre…
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Technische Universität Ilmenau（伊尔默瑙工业大学）
The hybrid zero dynamics control concept for bipedal walking is extended to include a non-instantaneous double support phase. A symmetric robot that consists of five rigid body segments which are connected by four actuated revolute joints is considered. Periodic walking gaits with a constant average walking speed consists of alternating single (SSP) and double support phases (DSP). Hybrid zero dynamics control designs usually assume an instantaneous DSP, which is a severe limitation. The proposed controllers use continuous SSPs and DSPs. Transitions between both phases are modeled as instantan…
Ohio State University（俄亥俄州立大学）；University of Michigan（密歇根大学）
The design of feedback controllers for bipedal robots is challenging due to the hybrid nature of its dynamics and the complexity imposed by high-dimensional bipedal models. In this paper, we present a novel approach for the design of feedback controllers using Reinforcement Learning (RL) and Hybrid Zero Dynamics (HZD). Existing RL approaches for bipedal walking are inefficient as they do not consider the underlying physics, often requires substantial training, and the resulting controller may not be applicable to real robots. HZD is a powerful tool for bipedal control with local stability guar…
University of Innsbruck（因斯布鲁克大学）；University of Hamburg（汉堡大学）
The complexity of bipedal locomotion may be attributed to the difficulty in synchronizing joint movements while at the same time achieving high-level objectives such as walking in a particular direction. Artificial central pattern generators (CPGs) can produce synchronized joint movements and have been used in the past for bipedal locomotion. However, most existing CPG-based approaches do not address the problem of high-level control explicitly. We propose a novel hierarchical control mechanism for bipedal locomotion where an optimized CPG network is used for joint control and a neural network…
This paper presents a gait controller for bipedal robots to achieve highly agile walking over various terrains given local slope and friction cone information. Without these considerations, untimely impacts can cause a robot to trip and inadequate tangential reaction forces at the stance foot can cause slippages. We address these challenges by combining, in a novel manner, a model based on an Angular Momentum Linear Inverted Pendulum (ALIP) and a Model Predictive Control (MPC) foot placement planner that is executed by the method of virtual constraints. The process starts with abstracting from…
Wheeled-legged robots combine the efficiency of wheeled robots when driving on suitably flat surfaces and versatility of legged robots when stepping over or around obstacles. This paper introduces a planning and control framework to realise dynamic locomotion for wheeled biped robots. We propose the Cart-Linear Inverted Pendulum Model (Cart-LIPM) as a template model for the rolling motion and the under-actuated LIPM for contact changes while walking. The generated motion is then tracked by an inverse dynamic whole-body controller which coordinates all joints, including the wheels. The framewor…
We present a trajectory planning and control architecture for bipedal locomotion at a variety of speeds on a highly underactuated and compliant bipedal robot. A library of compliant walking trajectories are planned offline, and stored as compact arrays of polynomial coefficients for tracking online. The control implementation uses a floating-base inverse dynamics controller which generates dynamically consistent feedforward torques to realize walking using information obtained from the trajectory optimization. The effectiveness of the controller is demonstrated in simulation and on hardware fo…
IEETA / DETI University of Aveiro（阿威罗大学 IEETA / DETI）
Biped robots are inherently unstable because of their complex kinematics as well as dynamics. Despite the many research efforts in developing biped locomotion, the performance of biped locomotion is still far from the expectations. This paper proposes a model-based framework to generate stable biped locomotion. The core of this framework is an abstract dynamics model which is composed of three masses to consider the dynamics of stance leg, torso and swing leg for minimizing the tracking problems. According to this dynamics model, we propose a modular walking reference trajectories planner whic…
LISV, University of Versailles Saint-Quentin（凡尔赛圣康坦大学LISV实验室）
This paper describes experimental results regarding the real time implementation of continuous time recurrent neural networks (CTRNN) and the dynamic back-propagation through time (BPTT) algorithm for the on-line learning control laws. Experiments are carried out to control the balance of a biped robot prototype in its standing posture. The neural controller is trained to compensate for external perturbations by controlling the torso's joint motions. Algorithms are embedded in the real time electronic unit of the robot. On-line learning implementations are presented in detail. The results on l…
The LNM Institute of Information and Technology（LNM信息技术学院）
This paper addresses the design and development of an autonomous biped robot using master and worker combination of controllers. In addition, the bot is wirelessly controllable. The work presented here explains the walking pattern, system control and actuator control techniques for 10 Degree of Freedom (DOF) biped humanoid. Bi-pedal robots have better mobility than conventional wheeled robots, but they tend to topple easily. In order to walk stably in various environments, such as on rough terrain, up and down slopes, or in regions containing obstacles, it is necessary, that robot should adapt…
Developing robust walking controllers for bipedal robots is a challenging endeavor. Traditional model-based locomotion controllers require simplifying assumptions and careful modelling; any small errors can result in unstable control. To address these challenges for bipedal locomotion, we present a model-free reinforcement learning framework for training robust locomotion policies in simulation, which can then be transferred to a real bipedal Cassie robot. To facilitate sim-to-real transfer, domain randomization is used to encourage the policies to learn behaviors that are robust across variat…
Collaborative Robotics and Intelligent Systems Institute（协作机器人与智能系统研究院）；Oregon State University（俄勒冈州立大学）
Controlling a non-statically stable biped is a difficult problem largely due to the complex hybrid dynamics involved. Recent work has demonstrated the effectiveness of reinforcement learning (RL) for simulation-based training of neural network controllers that successfully transfer to real bipeds. The existing work, however, has primarily used simple memoryless network architectures, even though more sophisticated architectures, such as those including memory, often yield superior performance in other RL domains. In this work, we consider recurrent neural networks (RNNs) for sim-to-real biped …
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；Hong Kong Institute of Science & Innovation, Chinese Academy of Sciences（中国科学院香港创新研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Swing arms have an irreplaceable role in promoting highly dynamic locomotion on bipedal robots by a larger angular momentum control space from the viewpoint of biomechanics. Few bipedal robots utilize swing arms and its redundancy characteristic of multiple degrees of freedom due to the lack of appropriate locomotion control strategies to perfectly integrate modeling and control. This paper presents a kind of control strategy by modeling the bipedal robot as a flywheel-spring loaded inverted pendulum (F-SLIP) to extract characteristics of swing arms and using the whole-body controller (WBC) to…
The ability to realize nonlinear controllers with formal guarantees on dynamic robotic systems has the potential to enable more complex robotic behaviors -- yet, realizing these controllers is often practically challenging. To address this challenge, this paper presents the end-to-end realization of dynamic bipedal locomotion on an underactuated bipedal robot via hybrid zero dynamics and control Lyapunov functions. A compliant model of Cassie is represented as a hybrid system to set the stage for a trajectory optimization framework. With the goal of achieving a variety of walking speeds in all…
We present a framework to generate periodic trajectory references for a 3D under-actuated bipedal robot, using a linear inverted pendulum (LIP) based controller with adaptive neural regulation. We use the LIP template model to estimate the robot's center of mass (CoM) position and velocity at the end of the current step, and formulate a discrete controller that determines the next footstep location to achieve a desired walking profile. This controller is equipped on the frontal plane with a Neural-Network-based adaptive term that reduces the model mismatch between the template and physical rob…
University of Aveiro（阿威罗大学）；University of Porto（波尔图大学）
This paper proposes a modular framework to generate robust biped locomotion using a tight coupling between an analytical walking approach and deep reinforcement learning. This framework is composed of six main modules which are hierarchically connected to reduce the overall complexity and increase its flexibility. The core of this framework is a specific dynamics model which abstracts a humanoid's dynamics model into two masses for modeling upper and lower body. This dynamics model is used to design an adaptive reference trajectories planner and an optimal controller which are fully parametric…
We present a new walking foot-placement controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of the 3LP model, our proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. This control paradigm reacts to disturbances immediately and includes rule…
Robotics and Motion Laboratory (RAMlab), University of Michigan（密歇根大学机器人学与运动实验室）
In this paper, we optimize over the control parameter space of our planar-bipedal robot, RAMone, for stable and energetically economical walking at various speeds. We formulate this task as an episodic reinforcement learning problem and use Covariance Matrix Adaptation. The parameters we are interested in modifying include gains from our Hybrid Zero Dynamics style controller and from RAMone's low-level motor controllers.
In this paper, we propose a novel framework on force-and-moment-based Model Predictive Control (MPC) for dynamic legged robots. Specifically, we present a formulation of MPC designed for 10 degree-of-freedom (DoF) bipedal robots using simplified rigid body dynamics with input forces and moments. This MPC controller will calculate the optimal inputs applied to the robot, including 3-D forces and 2-D moments at each foot. These desired inputs will then be generated by mapping these forces and moments to motor torques of 5 actuators on each leg. We evaluate our proposed control design on physical…
In this paper, we devise methods for the multi- objective control of humanoid robots, a.k.a. prioritized whole- body controllers, that achieve efficiency and robustness in the algorithmic computations. We use a form of whole-body controllers that is very general via incorporating centroidal momentum dynamics, operational task priorities, contact re- action forces, and internal force constraints. First, we achieve efficiency by solving a quadratic program that only involves the floating base dynamics and the reaction forces. Second, we achieve computational robustness by relaxing task accelerat…
With the goal of moving towards implementation of increasingly dynamic behaviors on underactuated systems, this paper presents an optimization-based approach for solving full-body dynamics based controllers on underactuated bipedal robots. The primary focus of this paper is on the development of an alternative approach to the implementation of controllers utilizing control Lyapunov function based quadratic programs. This approach utilizes many of the desirable aspects from successful inverse dynamics based controllers in the literature, while also incorporating a variant of control Lyapunov fu…
Feedback Regularization and Geometric PID Control for Robust Stabilization of a Planar Three-link Hybrid Bipedal Walking Model
Department of Mechanical Engineering, University of Peradeniya（珀斯德尼亚大学机械工程系）；Postgraduate and Research Unit, Sri Lanka Technological Campus（斯里兰卡科技校园研究生与研究单位）；Department of Mechanical Engineering, Texas Tech University（德克萨斯技术大学机械工程系）
