Majid Khadiv

Ilyass Taouil, Michal Ciebelski, Shafeef Omar et al.

We present MotionDisco, a framework that discovers contact-rich, long-horizon humanoid loco-manipulation motions from scratch, without relying on teleoperation or motion retargeting from human demonstrations. This is challenging because the space of possible contact interactions grows combinatorially with the task horizon and the number of objects in the scene. MotionDisco enables rapid discovery of novel motions by coupling a large language model (LLM) guided evolutionary search over sequences of interactions with an efficient sequential kinodynamic trajectory optimizer and pruning strategy, enabling the rapid discovery of novel skills. Through extensive ablation studies, we show that our LLM-guided search discovers successful whole-body trajectories across several challenging long-horizon tasks. Finally, by training reinforcement learning tracking policies on the discovered trajectories, we transfer the motions to a real humanoid robot. This is the first work to discover and deploy long-horizon humanoid loco-manipulation skills entirely through automated evolutionary search. Supplementary videos of the experiments are available at: https://youtu.be/DHiVz34QYlw.

Elham Daneshmand, Shafeef Omar, Glen Berseth et al.

Sim-to-real transfer of locomotion policies often leads to performance degradation due to the inevitable sim-to-real gap. Naively fine-tuning these policies directly on hardware is problematic, as it poses risks of mechanical failure and suffers from high sample inefficiency. In this paper, we address the challenge of safely and efficiently fine-tuning reinforcement learning (RL) policies for dynamic locomotion tasks. Specifically, we focus on fine-tuning policies learned in simulation directly on hardware, while explicitly enforcing safety constraints. In doing so, we introduce SLowRL, a framework that combines Low-Rank Adaptation (LoRA) with training-time safety enforcement via a recovery policy. We evaluate our method both in simulation and on a real Unitree Go2 quadruped robot for jump and trot tasks. Experimental results show that our method achieves a $46.5\%$ reduction in fine-tuning time and near-zero safety violations compared to standard proximal policy optimization (PPO) baselines. Notably, we find that a rank-1 adaptation alone is sufficient to recover pre-trained performance in the real world, while maintaining stable and safe real-world fine-tuning. These results demonstrate the practicality of safe, efficient fine-tuning for dynamic real-world robotic applications.

Victor Dhedin, Ilyass Taouil, Shafeef Omar et al.

In this paper, we introduce DynaRetarget, a complete pipeline for retargeting human motions to humanoid control policies. The core component of DynaRetarget is a novel Sampling-Based Trajectory Optimization (SBTO) framework that refines imperfect kinematic trajectories into dynamically feasible motions. SBTO incrementally advances the optimization horizon, enabling optimization over the entire trajectory for long-horizon tasks. We validate DynaRetarget by successfully retargeting hundreds of humanoid-object demonstrations and achieving higher success rates than the state of the art. The framework also generalizes across varying object properties, such as mass, size, and geometry, using the same tracking objective. This ability to robustly retarget diverse demonstrations opens the door to generating large-scale synthetic datasets of humanoid loco-manipulation trajectories, addressing a major bottleneck in real-world data collection.

Yutong Chao, Xudong Sun, Konstantin Riedl et al.

In this paper, we study a consensus-based optimization method for nonconvex bi-level optimization, where the objective is to minimize an upper-level function over the set of global minimizers of a lower-level problem. The proposed approach is derivative-free, and constructs its consensus point via smooth quantile selection combined with a Gibbs-type Laplace approximation. We establish convergence guarantees for both the associated \textit{mean-field} dynamics and its \textit{finite-particle} approximation. In particular, under suitable assumptions on smooth quantile localization, error bounds, and stability, we show that the mean-field law reaches any arbitrary prescribed Wasserstein neighborhood of the target bi-level solution with an explicit exponential rate up to the hitting time. Numerical experiments on a two-dimensional constrained problem and neural network training further support the theoretical results.

Shafeef Omar, Majid Khadiv

We present a unified framework for multi-task locomotion and manipulation policy learning grounded in a contact-explicit representation. Instead of designing different policies for different tasks, our approach unifies the definition of a task through a sequence of contact goals--desired contact positions, timings, and active end-effectors. This enables leveraging the shared structure across diverse contact-rich tasks, leading to a single policy that can perform a wide range of tasks. In particular, we train a goal-conditioned reinforcement learning (RL) policy to realise given contact plans. We validate our framework on multiple robotic embodiments and tasks: a quadruped performing multiple gaits, a humanoid performing multiple biped and quadrupedal gaits, and a humanoid executing different bimanual object manipulation tasks. Each of these scenarios is controlled by a single policy trained to execute different tasks grounded in contacts, demonstrating versatile and robust behaviours across morphologically distinct systems. Our results show that explicit contact reasoning significantly improves generalisation to unseen scenarios, positioning contact-explicit policy learning as a promising foundation for scalable loco-manipulation. Video available at: https://youtu.be/idHx67oHHU0?si=qZJ7C0ujemXNWgA5

Elham Daneshmand, Majid Khadiv, Felix Grimminger et al.

In this paper, we present a novel two-level variable Horizon Model Predictive Control (VH-MPC) framework for bipedal locomotion. In this framework, the higher level computes the landing location and timing (horizon length) of the swing foot to stabilize the unstable part of the center of mass (CoM) dynamics, using feedback from the CoM states. The lower level takes into account the swing foot dynamics and generates dynamically consistent trajectories for landing at the desired time as close as possible to the desired location. To do that, we use a simplified model of the robot dynamics projected in swing foot space that takes into account joint torque constraints as well as the friction cone constraints of the stance foot. We show the effectiveness of our proposed control framework by implementing robust walking patterns on our torque-controlled and open-source biped robot, Bolt. We report extensive simulations and real robot experiments in the presence of various disturbances and uncertainties.

Manuel Wüthrich, Felix Widmaier, Felix Grimminger et al.

Dexterous object manipulation remains an open problem in robotics, despite the rapid progress in machine learning during the past decade. We argue that a hindrance is the high cost of experimentation on real systems, in terms of both time and money. We address this problem by proposing an open-source robotic platform which can safely operate without human supervision. The hardware is inexpensive (about \SI{5000}[\$]{}) yet highly dynamic, robust, and capable of complex interaction with external objects. The software operates at 1-kilohertz and performs safety checks to prevent the hardware from breaking. The easy-to-use front-end (in C++ and Python) is suitable for real-time control as well as deep reinforcement learning. In addition, the software framework is largely robot-agnostic and can hence be used independently of the hardware proposed herein. Finally, we illustrate the potential of the proposed platform through a number of experiments, including real-time optimal control, deep reinforcement learning from scratch, throwing, and writing.

Felix Grimminger, Avadesh Meduri, Majid Khadiv et al.

We present a new open-source torque-controlled legged robot system, with a low-cost and low-complexity actuator module at its core. It consists of a high-torque brushless DC motor and a low-gear-ratio transmission suitable for impedance and force control. We also present a novel foot contact sensor suitable for legged locomotion with hard impacts. A 2.2 kg quadruped robot with a large range of motion is assembled from eight identical actuator modules and four lower legs with foot contact sensors. Leveraging standard plastic 3D printing and off-the-shelf parts results in a lightweight and inexpensive robot, allowing for rapid distribution and duplication within the research community. We systematically characterize the achieved impedance at the foot in both static and dynamic scenarios, and measure a maximum dimensionless leg stiffness of 10.8 without active damping, which is comparable to the leg stiffness of a running human. Finally, to demonstrate the capabilities of the quadruped, we present a novel controller which combines feedforward contact forces computed from a kino-dynamic optimizer with impedance control of the center of mass and base orientation. The controller can regulate complex motions while being robust to environmental uncertainty.

Shahram Khorshidi, Ahmad Gazar, Nicholas Rotella et al.

State of the art legged robots are either capable of measuring torque at the output of their drive systems, or have transparent drive systems which enable the computation of joint torques from motor currents. In either case, this sensor modality is seldom used in state estimation. In this paper, we propose to use joint torque measurements to estimate the centroidal states of legged robots. To do so, we project the whole-body dynamics of a legged robot into the nullspace of the contact constraints, allowing expression of the dynamics independent of the contact forces. Using the constrained dynamics and the centroidal momentum matrix, we are able to directly relate joint torques and centroidal states dynamics. Using the resulting model as the process model of an Extended Kalman Filter (EKF), we fuse the torque measurement in the centroidal state estimation problem. Through real-world experiments on a quadruped robot with different gaits, we demonstrate that the estimated centroidal states from our torque-based EKF drastically improve the recovery of these quantities compared to direct computation.

Avadesh Meduri, Paarth Shah, Julian Viereck et al.

Online planning of whole-body motions for legged robots is challenging due to the inherent nonlinearity in the robot dynamics. In this work, we propose a nonlinear MPC framework, the BiConMP which can generate whole body trajectories online by efficiently exploiting the structure of the robot dynamics. BiConMP is used to generate various cyclic gaits on a real quadruped robot and its performance is evaluated on different terrain, countering unforeseen pushes and transitioning online between different gaits. Further, the ability of BiConMP to generate non-trivial acyclic whole-body dynamic motions on the robot is presented. The same approach is also used to generate various dynamic motions in MPC on a humanoid robot (Talos) and another quadruped robot (AnYmal) in simulation. Finally, an extensive empirical analysis on the effects of planning horizon and frequency on the nonlinear MPC framework is reported and discussed.

Mahrokh Ghoddousi Boroujeni, Elham Daneshmand, Ludovic Righetti et al.

In this paper, we propose a novel framework capable of generating various walking and running gaits for bipedal robots. The main goal is to relax the fixed center of mass (CoM) height assumption of the linear inverted pendulum model (LIPM) and generate a wider range of walking and running motions, without a considerable increase in complexity. To do so, we use the concept of virtual constraints in the centroidal space which enables generating motions beyond walking while keeping the complexity at a minimum. By a proper choice of these virtual constraints, we show that we can generate different types of walking and running motions. More importantly, enforcing the virtual constraints through feedback renders the dynamics linear and enables us to design a feedback control mechanism which adapts the next step location and timing in face of disturbances, through a simple quadratic program (QP). To show the effectiveness of this framework, we showcase different walking and running simulations of the biped robot Bolt in the presence of both environmental uncertainties and external disturbances.

Paarth Shah, Avadesh Meduri, Wolfgang Merkt et al.

In this paper we explore the use of block coordinate descent (BCD) to optimize the centroidal momentum dynamics for dynamically consistent multi-contact behaviors. The centroidal dynamics have recently received a large amount of attention in order to create physically realizable motions for robots with hands and feet while being computationally more tractable than full rigid body dynamics models. Our contribution lies in exploiting the structure of the dynamics in order to simplify the original non-convex problem into two convex subproblems. We iterate between these two subproblems for a set number of iterations or until a consensus is reached. We explore the properties of the proposed optimization method for the centroidal dynamics and verify in simulation that motions generated by our approach can be tracked by the quadruped Solo12. In addition, we compare our method to a recently proposed convexification using a sequence of convex relaxations as well as a more standard interior point method used in the off- the-shelf solver IPOPT to show that our approach finds similar, if not better, trajectories (in terms of cost), and is more than four times faster than both approaches. Finally, compared to previous approaches, we note its practicality due to the convex nature of each subproblem which allows our method to be used with any off-the-shelf quadratic programming solver.

Miroslav Bogdanovic, Majid Khadiv, Ludovic Righetti

We present a general, two-stage reinforcement learning approach to create robust policies that can be deployed on real robots without any additional training using a single demonstration generated by trajectory optimization. The demonstration is used in the first stage as a starting point to facilitate initial exploration. In the second stage, the relevant task reward is optimized directly and a policy robust to environment uncertainties is computed. We demonstrate and examine in detail the performance and robustness of our approach on highly dynamic hopping and bounding tasks on a quadruped robot.

Bilal Hammoud, Majid Khadiv, Ludovic Righetti

This paper addresses the problem of computing optimal impedance schedules for legged locomotion tasks involving complex contact interactions. We formulate the problem of impedance regulation as a trade-off between disturbance rejection and measurement uncertainty. We extend a stochastic optimal control algorithm known as Risk Sensitive Control to take into account measurement uncertainty and propose a formal way to include such uncertainty for unknown contact locations. The approach can efficiently generate optimal state and control trajectories along with local feedback control gains, i.e. impedance schedules. Extensive simulations demonstrate the capabilities of the approach in generating meaningful stiffness and damping modulation patterns before and after contact interaction. For example, contact forces are reduced during early contacts, damping increases to anticipate a high impact event and tracking is automatically traded-off for increased stability. In particular, we show a significant improvement in performance during jumping and trotting tasks with a simulated quadruped robot.

Avadesh Meduri, Majid Khadiv, Ludovic Righetti

Reactive stepping and push recovery for biped robots is often restricted to flat terrains because of the difficulty in computing capture regions for nonlinear dynamic models. In this paper, we address this limitation by using reinforcement learning to approximately learn the 3D capture region for such systems. We propose a novel 3D reactive stepper, The DeepQ stepper, that computes optimal step locations for walking at different velocities using the 3D capture regions approximated by the action-value function. We demonstrate the ability of the approach to learn stepping with a simplified 3D pendulum model and a full robot dynamics. Further, the stepper achieves a higher performance when it learns approximate capture regions while taking into account the entire dynamics of the robot that are often ignored in existing reactive steppers based on simplified models. The DeepQ stepper can handle non convex terrain with obstacles, walk on restricted surfaces like stepping stones and recover from external disturbances for a constant computational cost.

Alonso Marco, Dominik Baumann, Majid Khadiv et al.

In the past decade, numerous machine learning algorithms have been shown to successfully learn optimal policies to control real robotic systems. However, it is common to encounter failing behaviors as the learning loop progresses. Specifically, in robot applications where failing is undesired but not catastrophic, many algorithms struggle with leveraging data obtained from failures. This is usually caused by (i) the failed experiment ending prematurely, or (ii) the acquired data being scarce or corrupted. Both complicate the design of proper reward functions to penalize failures. In this paper, we propose a framework that addresses those issues. We consider failing behaviors as those that violate a constraint and address the problem of learning with crash constraints, where no data is obtained upon constraint violation. The no-data case is addressed by a novel GP model (GPCR) for the constraint that combines discrete events (failure/success) with continuous observations (only obtained upon success). We demonstrate the effectiveness of our framework on simulated benchmarks and on a real jumping quadruped, where the constraint threshold is unknown a priori. Experimental data is collected, by means of constrained Bayesian optimization, directly on the real robot. Our results outperform manual tuning and GPCR proves useful on estimating the constraint threshold.

Mohammad Hasan Yeganegi, Majid Khadiv, Andrea Del Prete et al.

Model predictive control (MPC) has shown great success for controlling complex systems such as legged robots. However, when closing the loop, the performance and feasibility of the finite horizon optimal control problem (OCP) solved at each control cycle is not guaranteed anymore. This is due to model discrepancies, the effect of low-level controllers, uncertainties and sensor noise. To address these issues, we propose a modified version of a standard MPC approach used in legged locomotion with viability (weak forward invariance) guarantees. In this approach, instead of adding a (conservative) terminal constraint to the problem, we propose to use the measured state projected to the viability kernel in the OCP solved at each control cycle. Moreover, we use past experimental data to find the best cost weights, which measure a combination of performance, constraint satisfaction robustness, or stability (invariance). These interpretable costs measure the trade off between robustness and performance. For this purpose, we use Bayesian optimization (BO) to systematically design experiments that help efficiently collect data to learn a cost function leading to robust performance. Our simulation results with different realistic disturbances (i.e. external pushes, unmodeled actuator dynamics and computational delay) show the effectiveness of our approach to create robust controllers for humanoid robots.

Brahayam Ponton, Majid Khadiv, Avadesh Meduri et al.

This paper investigates the problem of efficient computation of physically consistent multi-contact behaviors. Recent work showed that under mild assumptions, the problem could be decomposed into simpler kinematic and centroidal dynamic optimization problems. Based on this approach, we propose a general convex relaxation of the centroidal dynamics leading to two computationally efficient algorithms based on iterative resolutions of second order cone programs. They optimize centroidal trajectories, contact forces and, importantly, the timing of the motions. We include the approach in a kino-dynamic optimization method to generate full-body movements. Finally, the approach is embedded in a mixed-integer solver to further find dynamically consistent contact sequences. Extensive numerical experiments demonstrate the computational efficiency of the approach, suggesting that it could be used in a fast receding horizon control loop. Executions of the planned motions on simulated humanoids and quadrupeds and on a real quadruped robot further show the quality of the optimized motions.

Ahmad Gazar, Majid Khadiv, Andrea Del Prete et al.

Linear Model Predictive Control (MPC) has been successfully used for generating feasible walking motions for humanoid robots. However, the effect of uncertainties on constraints satisfaction has only been studied using Robust MPC (RMPC) approaches, which account for the worst-case realization of bounded disturbances at each time instant. In this letter, we propose for the first time to use linear stochastic MPC (SMPC) to account for uncertainties in bipedal walking. We show that SMPC offers more flexibility to the user (or a high level decision maker) by tolerating small (user-defined) probabilities of constraint violation. Therefore, SMPC can be tuned to achieve a constraint satisfaction probability that is arbitrarily close to 100\%, but without sacrificing performance as much as tube-based RMPC. We compare SMPC against RMPC in terms of robustness (constraint satisfaction) and performance (optimality). Our results highlight the benefits of SMPC and its interest for the robotics community as a powerful mathematical tool for dealing with uncertainties.

Miroslav Bogdanovic, Majid Khadiv, Ludovic Righetti

Reinforcement learning algorithms have shown great success in solving different problems ranging from playing video games to robotics. However, they struggle to solve delicate robotic problems, especially those involving contact interactions. Though in principle a policy directly outputting joint torques should be able to learn to perform these tasks, in practice we see that it has difficulty to robustly solve the problem without any given structure in the action space. In this paper, we investigate how the choice of action space can give robust performance in presence of contact uncertainties. We propose learning a policy giving as output impedance and desired position in joint space and compare the performance of that approach to torque and position control under different contact uncertainties. Furthermore, we propose an additional reward term designed to regularize these variable impedance control policies, giving them interpretability and facilitating their transfer to real systems. We present extensive experiments in simulation of both floating and fixed-base systems in tasks involving contact uncertainties, as well as results for running the learned policies on a real system.

Mohammad Hasan Yeganegi, Majid Khadiv, S. Ali A. Moosavian et al.

Trajectory optimization (TO) is one of the most powerful tools for generating feasible motions for humanoid robots. However, including uncertainties and stochasticity in the TO problem to generate robust motions can easily lead to intractable problems. Furthermore, since the models used in TO have always some level of abstraction, it can be hard to find a realistic set of uncertainties in the model space. In this paper we leverage a sample-efficient learning technique (Bayesian optimization) to robustify TO for humanoid locomotion. The main idea is to use data from full-body simulations to make the TO stage robust by tuning the cost weights. To this end, we split the TO problem into two phases. The first phase solves a convex optimization problem for generating center of mass (CoM) trajectories based on simplified linear dynamics. The second stage employs iterative Linear-Quadratic Gaussian (iLQG) as a whole-body controller to generate full body control inputs. Then we use Bayesian optimization to find the cost weights to use in the first stage that yields robust performance in the simulation/experiment, in the presence of different disturbance/uncertainties. The results show that the proposed approach is able to generate robust motions for different sets of disturbances and uncertainties.

Majid Khadiv, Mohammad Hasan Yeganegi, S. Ali A. Moosavian et al.

Trajectory optimization (TO) is one of the most powerful tools for generating feasible motions for humanoid robots. However, including uncertainties and stochasticity in the TO problem to generate robust motions can easily lead to an interactable problem. Furthermore, since the models used in the TO have always some level of abstraction, it is hard to find a realistic set of uncertainty in the space of abstract model. In this paper we aim at leveraging a sample-efficient learning technique (Bayesian optimization) to robustify trajectory optimization for humanoid locomotion. The main idea is to use Bayesian optimization to find the optimal set of cost weights which compromises performance with respect to robustness with a few realistic simulation/experiment. The results show that the proposed approach is able to generate robust motions for different set of disturbances and uncertainties.

Reihaneh Mirjalili, Aghil Yousefi-koma, Farzad A. Shirazi et al.

In this paper, we present an approach for generating a variety of whole-body motions for a humanoid robot. We extend the available Model Predictive Control (MPC) approaches for walking on flat terrain to plan for both vertical motion of the Center of Mass (CoM) and external contact forces consistent with a given task. The optimization problem is comprised of three stages, i. e. the CoM vertical motion, joint angles, and contact forces planning. The choice of external contact (e. g. hand contact with the object or environment) among all available locations and the appropriate time to reach and maintain a contact are all computed automatically within the algorithm. The presented algorithm benefits from the simplicity of the Linear Inverted Pendulum Model (LIPM), while it overcomes the common limitations of this model and enables us to generate a variety of whole-body motions through external contacts. Simulation and experimental implementation of several whole-body actions in multi-contact scenarios on a humanoid robot show the capability of the proposed algorithm.

Fatemeh Nazemi, Aghil Yousefi-koma, Farzad A. shirazi et al.

Available possibilities to prevent a biped robot from falling down in the presence of severe disturbances are mainly Center of Pressure (CoP) modulation, step location and timing adjustment, and angular momentum regulation. In this paper, we aim at designing a walking pattern generator which employs an optimal combination of these tools to generate robust gaits. In this approach, first, the next step location and timing are decided consistent with the commanded walking velocity and based on the Divergent Component of Motion (DCM) measurement. This stage which is done by a very small-size Quadratic Program (QP) uses the Linear Inverted Pendulum Model (LIPM) dynamics to adapt the switching contact location and time. Then, consistent with the first stage, the LIPM with flywheel dynamics is used to regenerate the DCM and angular momentum trajectories at each control cycle. This is done by modulating the CoP and Centroidal Momentum Pivot (CMP) to realize a desired DCM at the end of current step. Simulation results show the merit of this reactive approach in generating robust and dynamically consistent walking patterns.

Majid Khadiv, S. Ali A. Moosvian, Aghil Yousefi-Koma et al.

Contact modeling plays a central role in motion planning, simulation, and control of legged robots, as legged locomotion is realized through contact. The two prevailing approaches to model the contact consider rigid and compliant premise at interaction ports. Contrary to the dynamics model of legged systems with rigid contact (without impact) which is straightforward to develop, there is no consensus among researchers to employ a standard compliant contact model. Our main goal in this paper is to study the dynamics model structure of bipedal walking systems with a rigid contact and a \textit{novel} compliant contact model and to present experimental validation of both models. For the model with rigid contact, after developing the model of the articulated bodies in flight phase without any contact with the environment, we apply the holonomic constraints at contact points and develop a constrained dynamics model of the robot in both single and double support phases. For the model with compliant contact, we propose a novel nonlinear contact model and simulate the motion of the robot using this model. In order to show the performance of the developed models, we compare obtained results from these models to the empirical measurements from bipedal walking of the human-sized humanoid robot SURENA III, which has been designed and fabricated at CAST, University of Tehran. This analysis shows the merit of both models in estimating dynamic behavior of the robot walking on a semi-rigid surface. The model with rigid contact, which is less complex and independent of the physical properties of the contacting bodies, can be employed for model-based motion optimization, analysis as well as control, while the model with compliant contact and more complexity is suitable for more realistic simulation scenarios.

Majid Khadiv, S. Ali A. Moosavian, Alexander Herzog et al.

In this paper, we extend state of the art Model Predictive Control (MPC) approaches to generate safe bipedal walking on slippery surfaces. In this setting, we formulate walking as a trade off between realizing a desired walking velocity and preserving robust foot-ground contact. Exploiting this formulation inside MPC, we show that safe walking on various flat terrains can be achieved by compromising three main attributes, i. e. walking velocity tracking, the Zero Moment Point (ZMP) modulation, and the Required Coefficient of Friction (RCoF) regulation. Simulation results show that increasing the walking velocity increases the possibility of slippage, while reducing the slippage possibility conflicts with reducing the tip-over possibility of the contact and vice versa.

Majid Khadiv, Alexander Herzog, S. Ali A. Moosavian et al.

Step adjustment can improve the gait robustness of biped robots, however the adaptation of step timing is often neglected as it gives rise to non-convex problems when optimized over several footsteps. In this paper, we argue that it is not necessary to optimize walking over several steps to ensure gait viability and show that it is sufficient to merely select the next step timing and location. Using this insight, we propose a novel walking pattern generator that optimally selects step location and timing at every control cycle. Our approach is computationally simple compared to standard approaches in the literature, yet guarantees that any viable state will remain viable in the future. We propose a swing foot adaptation strategy and integrate the pattern generator with an inverse dynamics controller that does not explicitly control the center of mass nor the foot center of pressure. This is particularly useful for biped robots with limited control authority over their foot center of pressure, such as robots with point feet or passive ankles. Extensive simulations on a humanoid robot with passive ankles demonstrate the capabilities of the approach in various walking situations, including external pushes and foot slippage, and emphasize the importance of step timing adaptation to stabilize walking.

Majid Khadiv, S. Ali. A. Moosavian, Aghil Yousefi-Koma et al.

In this paper, an online adaptation algorithm for bipedal walking on uneven surfaces with height uncertainty is proposed. In order to generate walking patterns on flat terrains, the trajectories in the task space are planned to satisfy the dynamic balance and slippage avoidance constraints, and also to guarantee smooth landing of the swing foot. To ensure smooth landing of the swing foot on surfaces with height uncertainty, the preplanned trajectories in the task space should be adapted. The proposed adaptation algorithm consists of two stages. In the first stage, once the swing foot reaches its maximum height, the supervisory control is initiated until the touch is detected. After the detection, the trajectories in the task space are modified to guarantee smooth landing. In the second stage, this modification is preserved during the Double Support Phase (DSP), and released in the next Single Support Phase (SSP). Effectiveness of the proposed online adaptation algorithm is experimentally verified through realization of the walking patterns on the SURENA III humanoid robot, designed and fabricated at CAST. The walking is tested on a surface with various flat obstacles, where the swing foot is prone to either land on the ground soon or late.

Milad Shafiee-Ashtiani, Aghil Yousefi-Koma, Masoud Shariat-Panahi et al.

The three bio-inspired strategies that have been used for balance recovery of biped robots are the ankle, hip and stepping Strategies. However, there are several cases for a biped robot where stepping is not possible, e. g. when the available contact surfaces are limited. In this situation, the balance recovery by modulating the angular momentum of the upper body (Hip-strategy) or the Zero Moment Point (ZMP) (Ankle strategy) is essential. In this paper, a single Model Predictive Control (MPC) scheme is employed for controlling the Capture Point (CP) to a desired position by modulating both the ZMP and the Centroidal Moment Pivot (CMP). The goal of the proposed controller is to control the CP, employing the CMP when the CP is out of the support polygon, and/or the ZMP when the CP is inside the support polygon. The proposed algorithm is implemented on an abstract model of the SURENA III humanoid robot. Obtained results show the effectiveness of the proposed approach in the presence of severe pushes, even when the support polygon is shrunken to a point or a line.

Majid Khadiv, Alexander Herzog, S. Ali. A. Moosavian et al.

Step adjustment for humanoid robots has been shown to improve robustness in gaits. However, step duration adaptation is often neglected in control strategies. In this paper, we propose an approach that combines both step location and timing adjustment for generating robust gaits. In this approach, step location and step timing are decided, based on feedback from the current state of the robot. The proposed approach is comprised of two stages. In the first stage, the nominal step location and step duration for the next step or a previewed number of steps are specified. In this stage which is done at the start of each step, the main goal is to specify the best step length and step duration for a desired walking speed. The second stage deals with finding the best landing point and landing time of the swing foot at each control cycle. In this stage, stability of the gaits is preserved by specifying a desired offset between the swing foot landing point and the Divergent Component of Motion (DCM) at the end of current step. After specifying the landing point of the swing foot at a desired time, the swing foot trajectory is regenerated at each control cycle to realize desired landing properties. Simulation on different scenarios shows the robustness of the generated gaits from our proposed approach compared to the case where no timing adjustment is employed.

Majid Khadiv, Sebastien Kleff, Alexander Herzog et al.

In this paper, a method for stabilizing biped robots stepping by a combination of Divergent Component of Motion (DCM) tracking and step adjustment is proposed. In this method, the DCM trajectory is generated, consistent with the predefined footprints. Furthermore, a swing foot trajectory modification strategy is proposed to adapt the landing point, using DCM measurement. In order to apply the generated trajectories to the full robot, a Hierarchical Inverse Dynamics (HID) is employed. The HID enables us to use different combinations of the DCM tracking and step adjustment for stabilizing different biped robots. Simulation experiments on two scenarios for two different simulated robots, one with active ankles and the other with passive ankles, are carried out. Simulation results demonstrate the effectiveness of the proposed method for robots with both active and passive ankles.