Humans plan for the near future to walk economically on uneven terrain

Humans experience small fluctuations in their gait when walking on uneven terrain. The fluctuations deviate from the steady, energy-minimizing pattern for level walking and have no obvious organization. But humans often look ahead when they walk, and could potentially plan anticipatory fluctuations for the terrain. Such planning is only sensible if it serves some an objective purpose, such as maintaining constant speed or reducing energy expenditure, that is also attainable within finite planning capacity. Here, we show that humans do plan and perform optimal control strategies on uneven terrain. Rather than maintaining constant speed, they make purposeful, anticipatory speed adjustments that are consistent with minimizing energy expenditure. A simple optimal control model predicts economical speed fluctuations that agree well with experiments with humans (N = 12) walking on seven different terrain profiles (correlated with model [Formula: see text] , [Formula: see text] all terrains). Participants made repeatable speed fluctuations starting about six to eight steps ahead of each terrain feature (up to ±7.5 cm height difference each step, up to 16 consecutive features). Nearer features matter more, because energy is dissipated with each succeeding step's collision with ground, preventing momentum from persisting indefinitely. A finite horizon of continuous look-ahead and motor working space thus suffice to practically optimize for any length of terrain. Humans reason about walking in the near future to plan complex optimal control sequences.

Multi-expert synthesis for versatile locomotion and manipulation skills

This work focuses on generating multiple coordinated motor skills for intelligent systems and studies a Multi-Expert Synthesis (MES) approach to achieve versatile robotic skills for locomotion and manipulation. MES embeds and uses expert skills to solve new composite tasks, and is able to synthesise and coordinate different and multiple skills smoothly. We proposed essential and effective design guidelines for training successful MES policies in simulation, which were deployed on both floating- and fixed-base robots. We formulated new algorithms to systematically determine task-relevant state variables for each individual experts which improved robustness and learning efficiency, and an explicit enforcement objective to diversify skills among different experts. The capabilities of MES policies were validated in both simulation and real experiments for locomotion and bi-manual manipulation. We demonstrated that the MES policies achieved robust locomotion on the quadruped ANYmal by fusing the gait recovery and trotting skills. For object manipulation, the MES policies learned to first reconfigure an object in an ungraspable pose and then grasp it through cooperative dual-arm manipulation.

Dynamic Balancing of Humanoid Robot with Proprioceptive Actuation: Systematic Design of Algorithm, Software, and Hardware

For humanoid robots, maintaining a dynamic balance against uncertain disturbance is crucial, and this function can be achieved by coordinating the whole body to perform multiple tasks simultaneously. Researchers generally accept hierarchical whole-body control (WBC) to address this function. Although experts can build feasible hierarchies using prior knowledge, real-time WBC is still challenging because it often requires a quadratic program with multiple inequality constraints. In addition, the torque tracking performance of the WBC algorithm will be affected by uncertain factors such as joint friction for a large transmission ratio proprioceptive-actuated robot. Therefore, the balance control of physical robots requires a systematic solution. In this study, a robot control system with high computing power and real-time communication ability, UBTMaster, is implemented to achieve a reduced WBC in real time. Based on these, a whole-body control scheme based on task priority for the dynamic balance of humanoid robots is implemented. After realizing the joint friction model identification, finally, a variety of balancing scenarios are tested on the Walker3 humanoid robot driven by the proprioceptive actuators to verify the effectiveness of the proposed scheme. The Walker3 robot exhibits excellent balance when multiple external disturbances occur simultaneously. For example, the two feet of the robot are subjected to tilt and displacement perturbations, respectively, while the torso is subjected to external shocks simultaneously. The experimental results show that the dynamic balance of the robot under multiple external disturbances can be achieved by using strictly hierarchical real-time WBC with a systematic design.

Adaptive robot climbing with magnetic feet in unknown slippery structure

Firm foot contact is the top priority of climbing robots to avoid catastrophic events, especially when working at height. This study proposes a robust planning and control framework for climbing robots that provides robustness to slippage in unknown environments. The framework includes 1) a center of mass (CoM) trajectory optimization under the estimated contact condition, 2) Kalman filter–like approach for uncertain environment parameter estimation and subsequent CoM trajectory re-planing, and 3) an online weight adaptation approach for whole-body control (WBC) framework that can adjust the ground reaction force (GRF) distribution in real time. Though the friction and adhesion characteristics are often assumed to be known, the presence of several factors that lead to a reduction in adhesion may cause critical problems for climbing robots. To address this issue safely and effectively, this study suggests estimating unknown contact parameters in real time and using the evaluated contact information to optimize climbing motion. Since slippage is a crucial behavior and requires instant recovery, the computation time for motion re-planning is also critical. The proposed CoM trajectory optimization algorithm achieved state-of-art fast computation via trajectory parameterization with several reasonable assumptions and linear algebra tricks. Last, an online weight adaptation approach is presented in the study to stabilize slippery motions within the WBC framework. This can help a robot to manage the slippage at the very last control step by redistributing the desired GRF. In order to verify the effectiveness of our method, we have tested our algorithm and provided benchmarks in simulation using a magnetic-legged climbing robot Manegto.

Gait multi-objectives optimization of lower limb exoskeleton robot based on BSO-EOLLFF algorithm

Aiming at problems of low optimization accuracy and slow convergence speed in the gait optimization algorithm of lower limb exoskeleton robot, a novel gait multi-objectives optimization strategy based on beetle swarm optimization (BSO)-elite opposition-based learning (EOL) levy flight foraging (LFF) algorithm was proposed. In order to avoid the algorithm from falling into the local optimum, the EOL strategy with global search capability, the LFF strategy with local search capability and the dynamic mutation strategy with high population diversity were introduced to improve optimization performance. The optimization was performed by establishing a multi-objectives optimization function with the robot’s gait zero moment point (ZMP) stability margin and driving energy consumption. The joint comparative tests were carried out in SolidWorks, ADAMS and MATLAB software. The simulation results showed that compared with the particle swarm optimization algorithm and the BSO algorithm, the ZMP stability margin obtained by the BSO-EOLLFF algorithm was increased, and the average driving energy consumption was reduced by 25.82% and 17.26%, respectively. The human-machine experiments were conducted to verify the effectiveness and superiority. The robot could realize stable and smooth walking with less energy consumption. This research will provide support for the application of exoskeleton robot.

Fast Online Optimization for Terrain-Blind Bipedal Robot Walking With a Decoupled Actuated SLIP Model

We present an online optimization algorithm which enables bipedal robots to blindly walk over various kinds of uneven terrains while resisting pushes. The proposed optimization algorithm performs high-level motion planning of footstep locations and center-of-mass height variations using the decoupled actuated spring-loaded inverted pendulum (aSLIP) model. The decoupled aSLIP model simplifies the original aSLIP with linear inverted pendulum (LIP) dynamics in horizontal states and spring dynamics in the vertical state. The motion planning can be formulated as a discrete-time model predictive control (MPC) problem and solved at a frequency of 1 kHz. The output of the motion planner is fed into an inverse-dynamics–based whole body controller for execution on the robot. A key result of this controller is that the feet of the robot are compliant, which further extends the robot’s ability to be robust to unobserved terrain variations. We evaluate our method in simulation with the bipedal robot SLIDER. The results show that the robot can blindly walk over various uneven terrains including slopes, wave fields, and stairs. It can also resist pushes of up to 40 N for a duration of 0.1 s while walking on uneven terrains.

Vision-Guided Six-Legged Walking of Little Crabster Using a Kinect Sensor

A conventional blind walking algorithm has low walking stability on uneven terrain because a robot cannot rapidly respond to height changes of the ground due to limited information from foot force sensors. In order to cope with rough terrain, it is essential to obtain 3D ground information. Therefore, this paper proposes a vision-guided six-legged walking algorithm for stable walking on uneven terrain. We obtained noise-filtered 3D ground information by using a Kinect sensor and experimentally derived coordinate transformation information between the Kinect sensor and robot body. While generating landing positions of the six feet from the predefined walking parameters, the proposed algorithm modifies the landing positions in terms of reliability and safety using the obtained 3D ground information. For continuous walking, we also propose a ground merging algorithm and successfully validate the performance of the proposed algorithms through walking experiments on a treadmill with obstacles.

Online Gain Adaptation of Whole-Body Control for Legged Robots with Unknown Disturbances

This paper proposes an online gain adaptation approach to enhance the robustness of whole-body control (WBC) framework for legged robots under unknown external force disturbances. Without properly accounting for external forces, the closed-loop control system incorporating WBC may become unstable, and therefore the desired task goals may not be achievable. To study the effects of external disturbances, we analyze the behavior of our current WBC framework via the use of both full-body and centroidal dynamics. In turn, we propose a way to adapt feedback gains for stabilizing the controlled system automatically. Based on model approximations and stability theory, we propose three conditions to ensure that the adjusted gains are suitable for stabilizing a robot under WBC. The proposed approach has four contributions. We make it possible to estimate the unknown disturbances without force/torque sensors. We then compute adaptive gains based on theoretic stability analysis incorporating the unknown forces at the joint actuation level. We demonstrate that the proposed method reduces task tracking errors under the effect of external forces on the robot. In addition, the proposed method is easy-to-use without further modifications of the controllers and task specifications. The resulting gain adaptation process is able to run in real-time. Finally, we verify the effectiveness of our method both in simulations and experiments using the bipedal robot Draco2 and the humanoid robot Valkyrie.

A bipedal walking robot that can fly, slackline, and skateboard

Numerous mobile robots in various forms specialize in either ground or aerial locomotion, whereas very few robots can perform complex locomotion tasks beyond simple walking and flying. We present the design and control of a multimodal locomotion robotic platform called LEONARDO, which bridges the gap between two different locomotion regimes of flying and walking using synchronized control of distributed electric thrusters and a pair of multijoint legs. By combining two distinct locomotion mechanisms, LEONARDO achieves complex maneuvers that require delicate balancing, such as walking on a slackline and skateboarding, which are challenging for existing bipedal robots. LEONARDO also demonstrates agile walking motions, interlaced with flying maneuvers to overcome obstacles using synchronized control of propellers and leg joints. The mechanical design and synchronized control strategy achieve a unique multimodal locomotion capability that could potentially enable robotic missions and operations that would be difficult for single-modal locomotion robots.

Efficient bipedal locomotion on rough terrain via compliant ankle actuation with energy regulation

Legged locomotion enables robotic platforms to traverse on rough terrain, which is quite challenging for other locomotion types, such as in wheeled and tracked systems. However, this benefit-moving robustly on rough terrain-comes with an inherent drawback due to the higher cost of transport in legged robots. The ultimate need for energy efficiency motivated the utilization of passive dynamics in legged locomotion. Nevertheless, a handicap in passive dynamic walking is the fragile basin of attraction that limits the locomotion capabilities of such systems. There have been various extensions to overcome such limitations by incorporating additional actuators and active control approaches at the expense of compromising the benefits of passivity. Here, we present a novel actuation and control framework, enabling efficient and sustained bipedal locomotion on significantly rough terrain. The proposed approach reinforces the passive dynamics by intermittent active feedback control within a bio-inspired compliant ankle actuation framework. Specifically, we use once-per-step energy regulation to adjust the spring precompression of the compliant ankle based on the liftoff instants-when the toe liftoffs from the ground-of the locomotion. Our results show that the proposed approach achieves highly efficient (with a cost of transport of 0.086) sustained locomotion on rough terrain, withstanding height variations up to 15% of the leg length. We provide theoretical and numerical analysis to demonstrate the performance of our approach, including systematic comparisons with the recent and state-of-the-art techniques in the literature.

Vertical Jumping for Legged Robot Based on Quadratic Programming

The highly dynamic legged jumping motion is a challenging research topic because of the lack of established control schemes that handle over-constrained control objectives well in the stance phase, which are coupled and affect each other, and control robot's posture in the flight phase, in which the robot is underactuated owing to the foot leaving the ground. This paper introduces an approach of realizing the cyclic vertical jumping motion of a planar simplified legged robot that formulates the jump problem within a quadratic-programming (QP)-based framework. Unlike prior works, which have added different weights in front of control tasks to express the relative hierarchy of tasks, in our framework, the hierarchical quadratic programming (HQP) control strategy is used to guarantee the strict prioritization of the center of mass (CoM) in the stance phase while split dynamic equations are incorporated into the unified quadratic-programming framework to restrict the robot's posture to be near a desired constant value in the flight phase. The controller is tested in two simulation environments with and without the flight phase controller, the results validate the flight phase controller, with the HQP controller having a maximum error of the CoM in the x direction and y direction of 0.47 and 0.82 cm and thus enabling the strict prioritization of the CoM.

Simulation of Upward Jump Control for One-Legged Robot Based on QP Optimization

An optimization framework for upward jumping motion based on quadratic programming (QP) is proposed in this paper, which can simultaneously consider constraints such as the zero moment point (ZMP), limitation of angular accelerations, and anti-slippage. Our approach comprises two parts: the trajectory generation and real-time control. In the trajectory generation for the launch phase, we discretize the continuous trajectories and assume that the accelerations between the two sampling intervals are constant and transcribe the problem into a nonlinear optimization problem. In the real-time control of the stance phase, the over-constrained control objectives such as the tracking of the center of moment (CoM), angle, and angular momentum, and constraints such as the anti-slippage, ZMP, and limitation of joint acceleration are unified within a framework based on QP optimization. Input angles of the actuated joints are thus obtained through a simple iteration. The simulation result reveals that a successful upward jump to a height of 16.4 cm was achieved, which confirms that the controller fully satisfies all constraints and achieves the control objectives.

Biped Walking Based on Stiffness Optimization and Hierarchical Quadratic Programming

The spring-loaded inverted pendulum model is similar to human walking in terms of the center of mass (CoM) trajectory and the ground reaction force. It is thus widely used in humanoid robot motion planning. A method that uses a velocity feedback controller to adjust the landing point of a robot leg is inaccurate in the presence of disturbances and a nonlinear optimization method with multiple variables is complicated and thus unsuitable for real-time control. In this paper, to achieve real-time optimization, a CoM-velocity feedback controller is used to calculate the virtual landing point. We construct a touchdown return map based on a virtual landing point and use nonlinear least squares to optimize spring stiffness. For robot whole-body control, hierarchical quadratic programming optimization is used to achieve strict task priority. The dynamic equation is given the highest priority and inverse dynamics are directly used to solve it, reducing the number of optimizations. Simulation and experimental results show that a force-controlled biped robot with the proposed method can stably walk on unknown uneven ground with a maximum obstacle height of 5 cm. The robot can recover from a 5 Nm disturbance during walking without falling.

Telelocomotion—Remotely Operated Legged Robots

Teleoperated systems enable human control of robotic proxies and are particularly amenable to inaccessible environments unsuitable for autonomy. Examples include emergency response, underwater manipulation, and robot assisted minimally invasive surgery. However, teleoperation architectures have been predominantly employed in manipulation tasks, and are thus only useful when the robot is within reach of the task. This work introduces the idea of extending teleoperation to enable online human remote control of legged robots, or telelocomotion, to traverse challenging terrain. Traversing unpredictable terrain remains a challenge for autonomous legged locomotion, as demonstrated by robots commonly falling in high-profile robotics contests. Telelocomotion can reduce the risk of mission failure by leveraging the high-level understanding of human operators to command in real-time the gaits of legged robots. In this work, a haptic telelocomotion interface was developed. Two within-user studies validate the proof-of-concept interface: (i) The first compared basic interfaces with the haptic interface for control of a simulated hexapedal robot in various levels of traversal complexity; (ii) the second presents a physical implementation and investigated the efficacy of the proposed haptic virtual fixtures. Results are promising to the use of haptic feedback for telelocomotion for complex traversal tasks.

Multi-expert learning of adaptive legged locomotion

Achieving versatile robot locomotion requires motor skills that can adapt to previously unseen situations. We propose a multi-expert learning architecture (MELA) that learns to generate adaptive skills from a group of representative expert skills. During training, MELA is first initialized by a distinct set of pretrained experts, each in a separate deep neural network (DNN). Then, by learning the combination of these DNNs using a gating neural network (GNN), MELA can acquire more specialized experts and transitional skills across various locomotion modes. During runtime, MELA constantly blends multiple DNNs and dynamically synthesizes a new DNN to produce adaptive behaviors in response to changing situations. This approach leverages the advantages of trained expert skills and the fast online synthesis of adaptive policies to generate responsive motor skills during the changing tasks. Using one unified MELA framework, we demonstrated successful multiskill locomotion on a real quadruped robot that performed coherent trotting, steering, and fall recovery autonomously and showed the merit of multi-expert learning generating behaviors that can adapt to unseen scenarios.

Robust and efficient forward, differential, and inverse kinematics using dual quaternions

Modern approaches for robot kinematics employ the product of exponentials formulation, represented using homogeneous transformation matrices. Quaternions over dual numbers are an established alternative representation; however, their use presents certain challenges: the dual quaternion exponential and logarithm contain a zero-angle singularity, and many common operations are less efficient using dual quaternions than with matrices. We present a new derivation of the dual quaternion exponential and logarithm that removes the singularity, we show an implicit representation of dual quaternions offers analytical and empirical efficiency advantages compared with both matrices and explicit dual quaternions, and we derive efficient dual quaternion forms of differential and inverse position kinematics. Analytically, implicit dual quaternions are more compact and require fewer arithmetic instructions for common operations, including chaining and exponentials. Empirically, we demonstrate a 30–40% speedup on forward kinematics and a 300–500% speedup on inverse position kinematics. This work relates dual quaternions with modern exponential coordinates and demonstrates that dual quaternions are a robust and efficient representation for robot kinematics.

Dynamic locomotion for passive-ankle biped robots and humanoids using whole-body locomotion control

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 article, we devise a new WBC, dubbed the 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 such that the control commands produce reduced jerk when switching foot contacts. To achieve robust dynamic locomotion, we conduct an in-depth analysis of uncertainty for our dynamic walking algorithm called the time-to-velocity-reversal (TVR) planner. The uncertainty study is fundamental as it allows us to improve the control algorithms and mechanical structure of our robot to fulfill the tolerated uncertainty. In addition, we conduct extensive experimentation for: (1) unsupported dynamic balancing (i.e., in-place stepping) with a six-degree-of-freedom biped, Mercury; (2) unsupported directional walking with Mercury; (3) walking over an irregular and slippery terrain with Mercury; and 4) in-place walking with our newly designed ten-DoF viscoelastic liquid-cooled biped, DRACO. Overall, the main contributions of this work are on: (a) achieving various modalities of unsupported dynamic locomotion of passive-ankle bipeds using a WBLC controller and a TVR planner; (b) conducting an uncertainty analysis to improve the mechanical structure and the controllers of Mercury; and (c) devising a whole-body control strategy that reduces movement jerk during walking.

Simulation of Disturbance Recovery Based on MPC and Whole-Body Dynamics Control of Biped Walking

Biped robots are similar to human beings and have broad application prospects in the fields of family service, disaster rescue and military affairs. However, simplified models and fixed center of mass (COM) used in previous research ignore the large-scale stability control ability implied by whole-body motion. The present paper proposed a two-level controller based on a simplified model and whole-body dynamics. In high level, a model predictive control (MPC) controller is implemented to improve zero moment point (ZMP) control performance. In low level, a quadratic programming optimization method is adopted to realize trajectory tracking and stabilization with friction and joint constraints. The simulation shows that a 12-degree-of-freedom force-controlled biped robot model, adopting the method proposed in this paper, can recover from a 40 Nm disturbance when walking at 1.44 km/h without adjusting the foot placement, and can walk on an unknown 4 cm high stairs and a rotating slope with a maximum inclination of 10°. The method is also adopted to realize fast walking up to 6 km/h.

A Benchmarking of DCM-Based Architectures for Position, Velocity and Torque-Controlled Humanoid Robots

This paper contributes toward the benchmarking of control architectures for bipedal robot locomotion. It considers architectures that are based on the Divergent Component of Motion (DCM) and composed of three main layers: trajectory optimization, simplified model control, and whole-body quadratic programming (QP) control layer. While the first two layers use simplified robot models, the whole-body QP control layer uses a complete robot model to produce either desired positions, velocities, or torques inputs at the joint-level. This paper then compares two implementations of the simplified model control layer, which are tested with position, velocity, and torque control modes for the whole-body QP control layer. In particular, both an instantaneous and a Receding Horizon controller are presented for the simplified model control layer. We show also that one of the proposed architectures allows the humanoid robot iCub to achieve a forward walking velocity of 0.3372[Formula: see text]m/s, which is the highest walking velocity achieved by the iCub robot.

Flexible model predictive control based on multivariable online adjustment mechanism for robust gait generation

The gait generation algorithm considering both step distance adjustment and step duration adjustment could improve the anti-disturbance ability of the humanoid robot, which is very important to the dynamic balance, but the step duration adjustment often brings non-convex optimization problems. In order to avoid this situation and improve the robustness of the gait generator, a gait generation mechanism based on flexible model predictive control is proposed in this article. Specifically, the step distance adjustment and step duration adjustment are set to be optimization objectives, while the change of pressure center is treated as the optimal input to minimize those objectives. With the current system state being used for online re-optimization, a feedback gait generator is formed to realize the strong stability of variable speed and variable step distance walking of the robot. The main contributions of this work are twofold. First, a gait generation mechanism based on flexible model predictive control is proposed, which avoids the problem of nonlinear optimization. Second, a variety of feasible optimization constraints were considered, they can be used on platforms with different computing resources. Simulations are conducted to verify the effectiveness of the proposed mechanism. Results show that as compared with those considering step adjustment only, the proposed method largely improves the compensation ability of disturbance and shortens the adjustment time.

A multi-objective evolutionary hyper-heuristic algorithm for team-orienteering problem with time windows regarding rescue applications

The team-orienteering problem (TOP) has broad applicability. Examples of possible uses are in factory and automation settings, robot sports teams, and urban search and rescue applications. We chose the rescue domain as a guiding example throughout this paper. Hence, this paper explores a practical variant of TOP with time window (TOPTW) for rescue applications by humanoid robots called TOPTWR. Due to the significant range of algorithm choices and their parameters tuning challenges, the use of hyper-heuristics is recommended. Hyper-heuristics can select, order, or generate different low-level heuristics with different optimization algorithms. In this paper, first, a general multi-objective (MO) solution is defined, with five objectives for TOPTWR. Then a robust and efficient MO and evolutionary hyper-heuristic algorithm for TOPTW based on the humanoid robot’s characteristics in the rescue applications (MOHH-TOPTWR) is proposed. MOHH-TOPTWR includes two MO evolutionary metaheuristics algorithms (MOEAs) known as non-dominated sorting genetic algorithm (NSGA-III) and MOEA based on decomposition (MOEA/D). In this paper, new benchmark instances are proposed for rescue applications using the existing ones for TOPTW. The experimental results show that MOHH-TOPTWR in both MOEAs can outperform all the state-of-the-art algorithms as well as NSGA-III and MOEA/D MOEAs.

Humanoid Locomotion Control and Generation Based on Contact Wrench Cones

This paper presents a general framework for locomotion control and generation of humanoid robots. Different from most of the existing work which uses the zero-moment point (2mp) to determine the feasibility of robot’s motion, we use the so-called contact wrench cone to derive motion feasibility conditions, whole-body motion controllers, and locomotion generators. The contact wrench cone consists of all feasible wrenches that can be applied to the robot through contacts, which provide allowable external forces and moments for realizing the robot’s motion. Algorithms are proposed to compute quantities defined on linear representations of a general convex cone, which can be various contact wrench cones as needed in developing motion generators and controllers. Based on the contact wrench cone for contact links and the proposed algorithms as well as a decomposition of the whole-body dynamics of a floating-base humanoid robot, we derive two motion tracking controllers. One controller contains a single quadratic program with linear inequality constraints, while the other consists of two quadratic programs which can be quickly solved by one of the proposed algorithms and in a closed form, respectively. Both controllers can be applied in real-time and achieve similar motion tracking performance in simulation. Based on contact wrench cones, furthermore, we derive two motion generation methods for humanoid robots. The first method adapts a reference motion, most often infeasible, to the robot by warping the motion’s time line so that the motion trajectory will remain the same but the velocity and acceleration profiles will be changed. The second method generates bipedal locomotion for given footsteps. All the proposed motion controllers and generators are applicable to general scenarios including uneven terrains and motions with the support of other links besides feet.

Bipedal walking and push recovery with a stepping strategy based on time-projection control

In this paper, we present a simple control framework for online push recovery on biped robots with dynamic stepping properties. Owing to relatively heavy legs in our humanoid robot COMAN, we use a linear model called 3LP, which is composed of three pendulums to take swing and torso dynamics into account. Based on 3LP equations, we formulate discrete linear quadratic regulator (LQR) controllers and use a particular time-projection method to adjust footstep locations during the motion continuously. This process, which is based on pelvis and swing foot tracking errors, naturally considers swing dynamics and leads to leg-retraction properties. Suggested adjustments are added to the Cartesian 3LP gaits and converted into joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies are also used to ensure enough ground clearance in perturbed walking conditions. The proposed control architecture is robust, yet uses very simple state estimation and basic position tracking. We rely on series elastic actuators to absorb impacts while introducing simple laws to compensate for spring compressions. Extensive experiments on COMAN (real) and Atlas (simulated) robots demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness with minimal reliance on the ankles and avoiding any active zero moment point (ZMP) control. The proposed architecture is therefore generic, computationally very fast and yet with no critical parameter to tune.

Robust Bipedal Locomotion Based on a Hierarchical Control Structure

To improve biped locomotion’s robustness to internal and external disturbances, this study proposes a hierarchical structure with three control levels. At the high level, a foothold sequence is generated so that the Center of Mass (CoM) trajectory tracks a planned path. The planning procedure is simplified by selecting the midpoint between two consecutive Center of Pressure (CoP) points as the feature point. At the middle level, a novel robust hybrid controller is devised to drive perturbed system states back to the nominal trajectory within finite cycles without chattering. The novelty lies in that the hybrid controller is not subject to linear CoM dynamic constraints. The hybrid controller consists of two sub-controllers: an oscillation controller and a smoothing controller. For the oscillation controller, the desired CoM height is specified as a sine-shaped function, avoiding a new attractive limit cycle. However, this controller results in the inevitable chattering because of discontinuities. A smoothing controller provides continuous properties and thus can inhibit the chattering problem, but has a smaller region of attraction compared with the oscillation controller. A hybrid controller merges the two controllers for a smooth transition. At the low level, the desired CoM motion is defined as tasks and embedded in a whole body operational space (WBOS) controller to compute the joint torques analytically. The novelty of the low-level controller lies in that within the WBOS framework, CoM motion is not subject to fixed CoM dynamics and thus can be generalized.

Dynamic bipedal locomotion over stochastic discrete terrain

Owing to their morphology and mechanical design, bipedal robots have the ability to traverse over a wide range of terrain including those with discrete footholds such as stepping stones. This paper addresses the challenge of planar dynamic robotic walking over stochastically generated stepping stones with significant variations in step length and step height, and where the robot has knowledge about the location of the next discrete foothold only one step ahead. Specifically, our approach utilizes a two-step periodic gait optimization technique to build a library of gaits parametrized by their resulting step lengths and step heights, as well as the initial configuration of the robot. By doing so, we address the problems involved during step transition when switching between the different walking gaits. We then use gait interpolation in real-time to obtain the desired gait. The proposed method is successfully validated on ATRIAS, an underactuated, human-scale bipedal robot, to achieve precise footstep placement. With no change in step height, step lengths are varied in the range of [23:78] cm. When both step length and step height are changed, their variation are within [30:65] cm and [−22:22] cm, respectively. The average walking speed of both these experiments is 0.6 m/s.