A Model Predictive Capture Point Control Framework for Robust Humanoid Balancing via Ankle, Hip, and Stepping Strategies

The robust balancing capability of humanoid robots against disturbances has been considered as one of the crucial requirements for their practical mobility in real-world environments. In particular, many studies have been devoted to the efficient implementation of the three balance strategies, inspired by human balance strategies involving ankle, hip, and stepping strategies, to endow humanoid robots with human-level balancing capability. In this paper, a robust balance control framework for humanoid robots is proposed. Firstly, a novel Model Predictive Control (MPC) framework is proposed for Capture Point (CP) tracking control, enabling the integration of ankle, hip, and stepping strategies within a single framework. Additionally, a variable weighting method is introduced that adjusts the weighting parameters of the Centroidal Angular Momentum (CAM) damping control over the time horizon of MPC to improve the balancing performance. Secondly, a hierarchical structure of the MPC and a stepping controller was proposed, allowing for the step time optimization. The robust balancing performance of the proposed method is validated through extensive simulations and real robot experiments. Furthermore, a superior balancing performance is demonstrated, particularly in the presence of disturbances, compared to a state-of-the-art Quadratic Programming (QP)-based CP controller that employs the ankle, hip, and stepping strategies. The supplementary video is available at https://youtu.be/CrD75UbYzdcComment: 19 pages,13 figure

ZMP Constraint Restriction for Robust Gait Generation in Humanoids

We present an extension of our previously proposed IS-MPC method for humanoid gait generation aimed at obtaining robust performance in the presence of disturbances. The considered disturbance signals vary in a range of known amplitude around a mid-range value that can change at each sampling time, but whose current value is assumed to be available. The method consists in modifying the stability constraint that is at the core of IS-MPC by incorporating the current mid-range disturbance, and performing an appropriate restriction of the ZMP constraint in the control horizon on the basis of the range amplitude of the disturbance. We derive explicit conditions for recursive feasibility and internal stability of the IS-MPC method with constraint modification. Finally, we illustrate its superior performance with respect to the nominal version by performing dynamic simulations on the NAO robot

Review of Anthropomorphic Head Stabilisation and Verticality Estimation in Robots

International audienceIn many walking, running, flying, and swimming animals, including mammals, reptiles, and birds, the vestibular system plays a central role for verticality estimation and is often associated with a head sta-bilisation (in rotation) behaviour. Head stabilisation, in turn, subserves gaze stabilisation, postural control, visual-vestibular information fusion and spatial awareness via the active establishment of a quasi-inertial frame of reference. Head stabilisation helps animals to cope with the computational consequences of angular movements that complicate the reliable estimation of the vertical direction. We suggest that this strategy could also benefit free-moving robotic systems, such as locomoting humanoid robots, which are typically equipped with inertial measurements units. Free-moving robotic systems could gain the full benefits of inertial measurements if the measurement units are placed on independently orientable platforms, such as a human-like heads. We illustrate these benefits by analysing recent humanoid robots design and control approaches

Benchmarking Dynamic Balancing Controllers for Humanoid Robots

This paper presents a comparison study of three control design approaches for humanoid balancing based on the Center of Mass (CoM) stabilization and body posture adjustment. The comparison was carried out under controlled circumstances allowing other researchers to replicate and compare our results with their own. The feedback control from state space design is based on simple models and provides sufficient robustness to control complex and high Degrees of Freedom (DoFs) systems, such as humanoids. The implemented strategies allow compliant behavior of the robot in reaction to impulsive or periodical disturbances, resulting in a smooth and human-like response while considering constraints. In this respect, we implemented two balancing strategies to compensate for the CoM deviation. The first one uses the robot’s capture point as a stability principle and the second one uses the Force/Torque sensors at the ankles to define a CoM reference that stabilizes the robot. In addition, was implemented a third strategy based on upper body orientation to absorb external disturbances and counterbalance them. Even though the balancing strategies are implemented independently, they can be merged to further increase balancing performance. The proposed strategies were previously applied on different humanoid bipedal platforms, however, their performance could not be properly benchmarked before. With this concern, this paper focuses on benchmarking in controlled scenarios to help the community in comparing different balance techniques. The key performance indicators (KPIs) used in our comparison are the CoM deviation, the settling time, the maximum measured orientation, passive gait measure, measured ankles torques, and reconstructed Center of Pressure (CoP). The benchmarking experiments were carried out in simulations and using the facility at Istituto Italiano di Tecnologia on the REEM-C humanoid robot provided by PAL robotics inside the EU H2020 project EUROBENCH framework

From walking to running: robust and 3D humanoid gait generation via MPC

Humanoid robots are platforms that can succeed in tasks conceived for humans. From locomotion in unstructured environments, to driving cars, or working in industrial plants, these robots have a potential that is yet to be disclosed in systematic every-day-life applications. Such a perspective, however, is opposed by the need of solving complex engineering problems under the hardware and software point of view. In this thesis, we focus on the software side of the problem, and in particular on locomotion control. The operativity of a legged humanoid is subordinate to its capability of realizing a reliable locomotion. In many settings, perturbations may undermine the balance and make the robot fall. Moreover, complex and dynamic motions might be required by the context, as for instance it could be needed to start running or climbing stairs to achieve a certain location in the shortest time. We present gait generation schemes based on Model Predictive Control (MPC) that tackle both the problem of robustness and tridimensional dynamic motions. The proposed control schemes adopt the typical paradigm of centroidal MPC for reference motion generation, enforcing dynamic balance through the Zero Moment Point condition, plus a whole-body controller that maps the generated trajectories to joint commands. Each of the described predictive controllers also feature a so-called stability constraint, preventing the generation of diverging Center of Mass trajectories with respect to the Zero Moment Point. Robustness is addressed by modeling the humanoid as a Linear Inverted Pendulum and devising two types of strategies. For persistent perturbations, a way to use a disturbance observer and a technique for constraint tightening (to ensure robust constraint satisfaction) are presented. In the case of impulsive pushes instead, techniques for footstep and timing adaptation are introduced. The underlying approach is to interpret robustness as a MPC feasibility problem, thus aiming at ensuring the existence of a solution for the constrained optimization problem to be solved at each iteration in spite of the perturbations. This perspective allows to devise simple solutions to complex problems, favoring a reliable real-time implementation. For the tridimensional locomotion, on the other hand, the humanoid is modeled as a Variable Height Inverted Pendulum. Based on it, a two stage MPC is introduced with particular emphasis on the implementation of the stability constraint. The overall result is a gait generation scheme that allows the robot to overcome relatively complex environments constituted by a non-flat terrain, with also the capability of realizing running gaits. The proposed methods are validated in different settings: from conceptual simulations in Matlab to validations in the DART dynamic environment, up to experimental tests on the NAO and the OP3 platforms

외란 및 토크 대역폭 제한을 고려한 토크 기반의 작업 공간 제어

학위논문(박사) -- 서울대학교대학원 : 융합과학기술대학원 융합과학부(지능형융합시스템전공), 2021.8. 박재흥.The thesis aims to improve the control performance of the torque-based operational space controller under disturbance and torque bandwidth limitation. Torque-based robot controllers command the desired torque as an input signal to the actuator. Since the torque is at force-level, the torque-controlled robot is more compliant to external forces from the environment or people than the position-controlled robot. Therefore, it can be used effectively for the tasks involving contact such as legged locomotion or human-robot interaction. Operational space control strengthens this advantage for redundant robots due to the inherent compliance in the null space of given tasks. However, high-level torque-based controllers have not been widely used for transitional robots such as industrial manipulators due to the low performance of precise control. One of the reasons is the uncertainty or disturbance in the kinematic and dynamic properties of the robot model. It leads to the inaccurate computation of the desired torque, deteriorating the control stability and performance. To estimate and compensate the disturbance using only proprioceptive sensors, the disturbance observer has been developed using inverse dynamics. It requires the joint acceleration information, which is noisy due to the numerical error in the second-order derivative of the joint position. In this work, a contact-consistent disturbance observer for a floating-base robot is proposed. The method uses the fixed contact position of the supporting foot as the kinematic constraints to estimate the joint acceleration error. It is incorporated into the dynamics model to reduce its effect on the disturbance torque solution, by which the observer becomes less dependent on the low-pass filter design. Another reason for the low performance of precise control is torque bandwidth limitation. Torque bandwidth is determined by the relationship between the input torque commanded to the actuator and the torque actually transmitted into the link. It can be regulated by various factors such as inner torque feedback loop, actuator dynamics, and joint elasticity, which deteriorates the control stability and performance. Operational space control is especially prone to this problem, since the limited bandwidth of a single actuator can reduce the performance of all related tasks simultaneously. In this work, an intuitive way to penalize low performance actuators is proposed for the operational space controller. The basic concept is to add joint torques only to high performance actuators recursively, which has the physical meaning of the joint-weighted torque solution considering each actuator performance. By penalizing the low performance actuators, the torque transmission error is reduced and the task performance is significantly improved. In addition, the joint trajectory is not required, which allows compliance in redundancy. The results of the thesis were verified by experiments using the 12-DOF biped robot DYROS-RED and the 7-DOF robot manipulator Franka Emika Panda.본 학위 논문은 외란과 토크 대역폭 제한이 존재할 때 토크 기반 작업 공간 제어기의 제어 성능을 높이는 것을 목표로 한다. 토크 기반의 로봇 제어기는 목표 토크를 입력 신호로서 구동기에 전달한다. 토크는 힘 레벨이기 때문에, 토크 제어 로봇은 위치 제어 로봇에 비해 외부 환경이나 사람으로부터 가해지는 외력에 더 유연하게 대응할 수 있다. 그러므로 토크 제어는 보행이나 인간-로봇 상호작용과 같은 접촉을 포함하는 작업을 위해 효과적으로 사용될 수 있다. 작업 공간 제어는 이러한 토크 제어의 장점을 더 강화시킬 수 있는데, 로봇이 여유 자유도가 있을 때 작업의 영공간에서 존재하는 모션들이 내재적으로 유연하기 때문이다. 그러나 이러한 장점에도 불구하고 토크 기반의 로봇 제어기는 정밀 제어 성능이 떨어지기 때문에 산업용 로봇 팔과 같은 전통적인 로봇에는 널리 사용되지 못했다. 그 이유 중 한 가지는 로봇 모델의 기구학 및 동역학 물성치에 존재하는 외란이다. 모델 오차는 목표 토크를 계산할 때 오차를 유발하며, 이것이 제어 안정성과 성능을 약화시키게 된다. 외란을 내재 센서만을 이용하여 추정 및 보상하기 위해 역동역학 기반의 외란 관측기가 개발되어 왔다. 외란 관측기는 역동역학 계산을 위해 관절 각가속도 정보가 필요한데, 이 값이 관절 위치를 두 번 미분한 값이기 때문에 수치적인 오차로 노이즈해지는 문제가 있었다. 본 연구에서는 부유형 기저 로봇을 위한 접촉 조건이 고려된 외란 관측기가 제안되었다. 제안된 방법은 로봇의 고정된 접촉 지점에 대한 기구학적인 구속 조건을 이용하여 관절 각가속도 오차를 추정한다. 추정된 오차를 동역학 모델에 반영하여 외란 토크를 계산함으로써 저역 통과 필터 성능에 대한 의존도를 줄일 수 있다. 토크 기반 제어의 정밀 제어 성능이 떨어지는 또 다른 이유 중 하나는 토크 대역폭 제한이다. 토크 대역폭은 구동기에 전달되는 입력 토크와 실제 링크에 전달되는 토크와의 관계로 결정된다. 토크 대역폭은 구동기 내부의 토크 피드백 루프, 구동기 동역학, 관절 탄성 등의 요인들에 의해 제한될 수 있는데 이것이 제어 안정성 및 성능을 감소시킨다. 작업 공간 제어는 특히 이 문제에 취약한데, 대역폭이 제한된 구동기 하나가 그와 연관된 모든 작업 공간의 제어 성능을 감소시킬 수 있기 때문이다. 본 연구에서는 작업 공간 제어기에서 성능이 낮은 구동기의 사용을 제한하기 위한 직관적인 전략이 제안되었다. 기본 컨셉은 작업 제어를 위한 토크 솔루션에 성능이 좋은 관절에만 추가적으로 토크 솔루션을 더해나가는 것으로, 이것은 각 관절의 가중치가 고려된 토크 솔루션이 되는 것을 의미한다. 성능이 낮은 구동기의 사용을 제한함으로써 토크 전달 오차가 줄어들고 작업 성능이 크게 향상될 수 있다. 본 학위 논문의 연구 결과들은 12자유도 이족 보행 로봇 DYROS-RED와 7자유도 로봇 팔 Franka Emika Panda를 이용한 실험을 통해 검증되었다.1 INTRODUCTION 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Contributions of Thesis . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 BACKGROUNDS 6 2.1 Operational Space Control . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Dynamics Formulation . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Fixed-Base Dynamics . . . . . . . . . . . . . . . . . . . . 9 2.2.1.1 Joint Space Formulation . . . . . . . . . . . . . 9 2.2.1.2 Operational Space Formulation . . . . . . . . . . 11 2.2.2 Floating-Base Dynamics . . . . . . . . . . . . . . . . . . . 12 2.2.2.1 Joint Space Formulation . . . . . . . . . . . . . 12 2.2.2.2 Operational Space Formulation . . . . . . . . . . 14 2.3 Position Tracking via PD Control . . . . . . . . . . . . . . . . . . 17 2.3.1 Torque Solution . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.2 Orientation Control . . . . . . . . . . . . . . . . . . . . . 19 3 CONTACT-CONSISTENT DISTURBANCE OBSERVER FOR FLOATING-BASE ROBOTS 22 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 Momentum-Based Disturbance Observer . . . . . . . . . . . . . . 24 3.3 The Proposed Method . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4.2 External Force Estimation . . . . . . . . . . . . . . . . . . 33 3.4.3 Internal Disturbance Rejection . . . . . . . . . . . . . . . 35 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 OPERATIONAL SPACE CONTROL UNDER ACTUATOR BANDWIDTH LIMITATION 40 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.2 The Proposed Method . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.2 OSF-Based Torque Solution . . . . . . . . . . . . . . . . . 45 4.2.3 Comparison With a Typical Method . . . . . . . . . . . . 47 4.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.4 Comparison With Other Approaches . . . . . . . . . . . . . . . . 61 4.4.1 Controller Formulation . . . . . . . . . . . . . . . . . . . . 62 4.4.1.1 The Proposed Method . . . . . . . . . . . . . . . 62 4.4.1.2 The OSF Controller . . . . . . . . . . . . . . . . 62 4.4.1.3 The OSF-Filter Controller . . . . . . . . . . . . 62 4.4.1.4 The OSF-Joint Controller . . . . . . . . . . . . . 67 4.4.1.5 The Joint Controller . . . . . . . . . . . . . . . . 68 4.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.5 Frequency Response of Joint Torque . . . . . . . . . . . . . . . . 72 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5 CONCLUSION 85 Abstract (In Korean) 100박

Active Disturbance Rejection Control based on Generalized Proportional Integral Observer to Control a Bipedal Robot with Five Degrees of Freedom

An Active Disturbance Rejection Control based on Generalized Proportional Integral observer (ADRC with GPI observer) was developed to control the gait of a bipedal robot with five degrees of freedom. The bipedal robot used is a passive point feet which produces an underactuated dynamic walking. A virtual holonomic constraint is imposed to generate online smooth trajectories which were used as references of the control system. The proposed control strategy is tested through numerical simulation on a task of forward walking with the robot exposed to external disturbances. The performance of ADRC with GPI observer strategy is compared with a feedback linearization with proportional-derivative control. A stability test consisting on analyzing the existence of limit cycles using the Poincaré's method revealed that asymptotically stable walking was achieved. The proposed control strategy effectively rejects the external disturbances and keeps the robot in a stable dynamic walking