S. Ali A. Moosavian

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.

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.

S. Ali A. Moosavian, Mahdi Nabipour, Farshid Absalan et al.

Utilizing orthoses and exoskeleton technology in various applications and medical industries, particularly to help elderly and ordinary people in their daily activities is a new growing field for research institutes. In this paper, after introducing an assistive lower limb exoskeleton (RoboWalk), the dynamics models of both multi-body kinematic tree structure human and robot is derived separately, using Newton's method. The obtained models are then verified by comparing the results with those of the Recursive Newton-Euler Algorithms (RNEA). These models are then augmented to investigate the RoboWalk joint torques, and those of the human body, and also the floor reaction force of the complete system. Since RoboWalk is an under-actuated robot, despite the assistive force, an undesirable disturbing force exerts to the human. So, optimization strategies are proposed to find an optimal design to maximize the assistive behavior of RoboWalk and reduce joint torques of the human body as a result. To this end, a human-in-the-loop optimization algorithm will be used. The solution of this optimization problem is carried out by Particle Swarm Optimization (PSO) method. The designed analysis and the optimization results demonstrate the effectiveness of the proposed approaches, leading to the elimination of disturbing forces, lower torque demand for RoboWalk motors and lower weights.

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.

Ali Zamani, Mahdi Khorram, S. Ali A. Moosavian

Synthesizing a stable gait that enables a quadruped robot to climb stairs is the focus of this paper. To this end, first a stable transition from initial to desired configuration is made based on the minimum number of steps and maximum use of the leg workspace to prepare the robot for the movement. Next, swing leg and body trajectories are planned for a successful stair- climbing gait. Afterwards, a stable spinning gait is proposed to change the orientation of the body. We simulate our gait planning algorithms on a model of quadruped robot. The results show that the robot is able to climb up stairs, rotate about its yaw axis, and climb down stairs while its stability is guaranteed.

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.

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.