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 are 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 tradeoff between robustness and performance. For this purpose, we use Bayesian optimization 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.

Step adjustment can improve the gait robustness of biped robots; however, the adaptation of step timing is often neglected as it gives rise to nonconvex problems when optimized over several footsteps. In this article, 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.

Heavy object manipulation by wheeled mobile manipulators may lead to serious consequences such as postural instability, and this necessitates dynamically stable planning based on systematic analysis to better predict and eliminate the possibility of toppling down. In the present study, stable motion planning is investigated for wheeled mobile manipulators during heavy object manipulation tasks. It is assumed that the initial and final poses of a heavy payload are specified. Based on these known postures of the payload two proper configurations for robotic system is defined. Then, between these two initial and final poses, appropriate trajectories for multiple robotic arms relative to the moving base are planned without considering the postural stability of the system. Next, motion of the moving base is planned so that the stability of the overall system is guaranteed while its predetermined initial and final positions and velocities are fulfilled. To this end, the problem of stable planning is solved as an optimization problem. A proper cost function is considered, to be minimized, which is a measure of the control effort to be used for the platform motion. Moreover, using the new dynamic postural Moment-Height Stability (MHS) measure, a constraint denoting the system dynamic stability is derived and satisfied. The proposed planning approach is applied to move a heavy object with a wheeled robotic system that consists of two manipulators, where the obtained results reveal a stable optimal motion besides satisfaction of various practical aspects.

Dynamics and control of a space robotic system with flexible members during an object manipulation task is studied here. Flexible members such as solar panels of space free flying robotic systems and their flexible joints during a manoeuvre may get stimulated and vibrate. Therefore, such vibrations will cause some oscillatory disturbance forces on the moving base and manipulated object, which in turn produces error in the position and speed of the manipulating end effectors. These flexible members are classified into active and passive elements, to study the ways of controlling the vibration effects of such members. In this paper, considering a multiple arm space robotic system with flexible joints and flexible solar panels, the system dynamics is partitioned into two rigid and flexible bodies' motion, and a practical model for control implementations on compounded rigid-flexible multi-body systems is developed. Then, based on a designated path/trajectory for a space robotic system, the multiple impedance control is extended to perform an object manipulation task by such complicated rigid-flexible multi body systems. Finally, a space free flying robotic system is simulated which contains two 2-DOF planar manipulators with flexible joints, and a rotating antenna and a camera as its third and fourth arm, appended with two solar panels. Obtained results reveal the merits of proposed controller to successfully perform the manipulation task and effectively suppress the vibration of flexible elements which will be discussed.

In this paper, a suspended mobile platform with two 3 DOF manipulators, is used to manipulate an object in a combined circular-straight path. The multiple impedance control (MIC) is used as a model-based algorithm which has been shown to have desirable performance in case of impact with an obstacle and system flexibility. The MIC enforces same impedance law both on the robotic system, and the manipulated object level. However, to apply model-based control laws, it is needed to extract system dynamics model. For such complicated robotic systems with suspension system, it is necessary to have a concise set of dynamic equations of motion with few mathematical calculations. Therefore, the concept of direct path method is extended to derive explicit dynamics modeling for such challenging systems. Then, non-holonomic constraint of the wheeled system is derived, and the obtained dynamics model is reformatted to become a more concise one using natural orthogonal complement method. Next, the MIC law is applied to cooperative manipulation of an object by two manipulators mounted on a suspended wheeled robotic system. The obtained results reveal a smooth system performance, i.e. negligible small tracking errors in the presence of impacts with obstacles and significant disturbances.

In this study, kinematics design, dynamics modeling and verification of a compounded serial-parallel wheeled mobile robot is elaborated. The proposed novel kinematic structure is best suited to fulfill stable motion of the robotic system when handling heavy objects by manipulators mounted on mobile platforms. The proposed system is made of a differentially-driven wheeled platform, a planar parallel manipulator, which is called here as Star-Triangle (ST) mechanism, and a serial Puma-type manipulator arm. The suggested structure adopts the advantages of both serial and parallel robots, to move the base point of the serial robot with respect to the mobile platform to fulfill the system stability after grasping heavy objects. In order to investigate the comprehensive kinematics model of the robot, after introducing its novel structure it is divided into three modules, i.e. a mobile platform, a parallel ST mechanism, and a serial robot. Next, a closed-form dynamics model is derived for the whole hybrid system based on a combined Newton-Euler and Lagrange formulation. The proposed method presents the mutual dynamic interaction wrenches between the integrated platform and the serial manipulator which can be exploited for the tip-over stability analysis of the mobile robotic system. Then, to verify the obtained mathematical model, several benchmark actuating inputs are applied to the model and the system responses are analyzed.

The modified transpose Jacobian (MTJ) algorithm is a recently proposed algorithm used in manipulator control. Based on an approximated feedback linearization approach the MTJ does not need to a priori knowledge of the plant dynamics. In this paper, this scheme is extended to the complicated control problem of underactuated robots in Cartesian space. Based on the notion of transpose effective Jacobian, this new proposed algorithm is called modified transpose effective Jacobian (MTEJ) algorithm. The MTEJ control law employs stored data of the control command in the previous time step, as a learning tool to yield an improved performance, with no substantial need to a priori knowledge of the plant dynamics. Therefore, unlike a model-based algorithm, it is almost not affected by inaccuracies in mass properties. The gains of the proposed MTEJ can be selected more systematically, and do not need to be large, hence the noise rejection characteristics of the algorithm are improved. Obtained results show an improved performance compared to that of the transpose effective Jacobian and even model-based algorithms.

Tracked mobile robots (TMRs) can be considered as the most important type of mobile robots. Large contact area of tracks with the ground provides superior advantages for TMRs such as better mobility in unstructured environments, though it may cause a higher risk of slippage. In this paper, an experimental slip model is proposed for exact kinematics modeling, and the parameters of this model will be determined based on experimental analysis of ResQuake. This is a tele-operative rescue mobile robot with great capabilities in climbing obstacles in destructed areas, and its performance was demonstrated in Rescue robot league of RoboCup 2005 in Osaka (Japan), achieving the 2ndbest design award, and RoboCup 2006 in Bremen (Germany) achieving the best operator interface award. Therefore, ResQuake is used here as an experimental platform to study the relationship between slippage of tracks and two main physically meaningful factors, i.e. radius of the tracking path and speed of the robot. The slip coefficients will be obtained as an exponential function of radius of curvature of the path. To validate the obtained results, the proposed model will be used along with two path tracking controllers, and it is empirically demonstrated that the developed model drastically improves the system performance in terms of lower path tracking errors.

Field Robots are machines that work in unstructured environments. Handling the mobility performance requirements of a challenging rough terrain makes a suspended wheeled mobile robot (SWMR), with multiple dexterous manipulators, an appropriate field robot design. In this study, first a general systematic procedure for dynamics modeling of such complicated systems is presented based on application of Newton-Euler's formulation for a chain of rigid bodies. Then, to verify the obtained dynamics model, another model for the considered system has been developed using ADAMS simulation software. Comparison between the results obtained from these two models confirms the thoroughness of the proposed analytical model. The presented approach can provide the interaction wrench(es) between the mobile base and the mounted arm(s). Next, using the obtained dynamics, the tip-over stability of such systems will be investigated. To this end, the new dynamic tip-over Moment- Height Stability (MHS) measure will be extended for suspended wheeled mobile robotic systems. Proposing the concept of virtual structure, the obtained planar model of SWMR has been employed to evaluate the behavior of the system on rough terrain in terms of its stability. Therefore the presented model and the MHS measure can be employed for stable planning and model-based control of autonomous SWMR during object manipulation tasks.

Mobile machines equipped with manipulator arm(s) are being increasingly used in a variety of areas of industry. When these mobile utilities perform fast maneuvers, move over rough terrain, manipulate heavy work pieces, or interact large wrenches with their environment, they may go unstable and overturn. Therefore, safety and efficiency of such systems can be improved with a reliable stability recognition metric. For on-line applications, such tip-over stability measure should be computationally simple which makes its presentation a challenging task. In this study, various dynamic stability measures are investigated and compared with each other in terms of their reliability and computational complexity. Then, a new reliable and efficient metric named as Moment-Height Stability (MHS) measure is introduced for mobile manipulators. The proposed metric is a physically meaningful and reliable measure while it contains low computational burden. The MHS measure can be exploited successfully for wheeled mobile manipulators containing single or multiple arms. Besides, by some minor modifications the MHS measure can be also employed for the case of legged locomotion. Also, the proposed MHS measure may be extended for the case of suspended mobile manipulator on rough terrains. Several case studies are presented to reveal the effectiveness of the new MHS measure compared to the main previous measures.

In this paper, considering Space Free-Flyer Robots as highly nonlinear coupled systems, a chattering avoidance sliding mode controller is developed with confined computational burden for on-line implementations. A regulating routine is proposed to determine proper positive values for the coefficient of sliding condition. In addition, to reduce the computational cost for on-line applications, an explicit direct relationship between the SFFR's actuators (force/torque) demands and measurement of distances from the corresponding sliding surfaces is proposed. Then this model is optimally parameterized using Prediction Error Method (PEM). Also, to achieve an acceptable performance, the parameters are estimated recursively using Kalman Filter as a parameter estimator. To this end, first an explicit dynamics model of a 14-DOF SFFR is derived via SPACEMAPLE where Recursive PEM method is used for parameterization of the SFFR model. Then, based on the estimated dynamics, a multi input sliding mode control law is applied to the given SFFR to catch a moving target. To evaluate the new proposed algorithm in a more complicated condition, it is assumed that for controlling the base of SFFR only on-off actuators are available, which can just generate a constant positive or negative force/torque. The obtained results show that the proposed regulated sliding mode controller can significantly alleviate the chattering trend, and consequently energy consumption will be substantially decreased as well as reduced computational burden with reasonable running time duration for on-line implementations.

This paper presents design and manufacturing procedure of a tele-operative rescue robot. First, the general task to be performed by such a robot is defined, and variant kinematic mechanisms to form the basic structure of the robot will be discussed. Choosing an appropriate mechanism, geometric dimensions, and mass properties will be detailed to develop a dynamics model for the system. Next, the strength of each component is analyzed to finalize its shape. To complete the design procedure, Patran/Nastran was used to apply the finite element method for strength analysis of complicated parts. Also, ADAMS was used to model the mechanisms, where 3D sketch of each component of the robot was generated by means of Solidworks, and several sets of equations governing the dimensions of system were solved using Matlab. Finally, the components are fabricated and assembled together with controlling hardware. Two main processors are used within the control system of the robot. The operator's PC as the master processor and the laptop installed on the robot as the slave processor. The performance of the system was demonstrated in Rescue robot league of RoboCup 2005 in Osaka (Japan) and achieved the 2nd best design award.

Multiple Impedance control (MIC) enforces designated impedance on all cooperating manipulators, the manipulated object, and the spacecraft of a space free flying robotic system to manipulate a grasped object, and move it on a desired path. However, during such maneuvers, some inner forces and torques are usually produced in the object. For tuning the inner object forces, it is needed to model the inner forces/torques or their effects on the object. In this paper, a virtual linkage model is introduced to determine the inner forces using the MIC law. Also, the load distribution between end-effectors is modeled. To this end, the MIC law is used to control both path tracking and inner forces tuning when manipulating an object. The moving object is grasped solidly with two 6 degrees of freedom (DOF) cooperating end-effectors mounted on a 6 DOF spacecraft appended with a 2 DOF antenna. An explicit dynamics model of this highly complicated 20 DOF system is derived using SPACEMAPLE, and then simulated in MATLAB. The MIC law controls the resulting deflection in the object due to tension or compression forces, also torsion and bending moments besides its motion on a desired path. The obtained results reveal good tracking performance of the proposed MIC controller, besides tuning the object internal forces.

Multiple impedance control (MIC) is an algorithm that enforces designated impedance on all cooperating manipulators, the manipulated object, and the moving base, if applied to a space (or mobile) robotic system. It has been shown that the MIC algorithm can also satisfy force-tracking requirements in object manipulation tasks. In this paper, the disturbance rejection characteristics of this algorithm applied to complicated space free-flying robotic systems is studied. The results of this analysis reveal that the effect of disturbances substantially reduces through appropriate tuning of the controller mass matrix gain. Using MAPLE and MATLAB tools, a system of three manipulators mounted on a space free-flyer with eight D.O.F. is simulated in which a Remote Center Compliance (RCC) is attached to the second end-effector, subjected to force and torque disturbances applied on several points. The simulation results reveal the merits of the MIC algorithm in terms of disturbance rejection characteristics, i.e. negligibly small errors in both position and force tracking in the presence of significant disturbances.

The new algorithm of multiple impedance control (MIC) which enforces designated impedance on both a manipulated object, and all cooperating manipulators is applied to a space robotic system in which robotic arms, mounted on a free-flying-base, manipulate an object. A vigorous stability analysis of the MIC algorithm based on Lyapunov direct method, besides error analysis, show that the MIC law guarantees good tracking of cooperative manipulators and the object, in performing a manipulation task. Also, a force tracking strategy inspired by human control system is added to the MIC algorithm and the general formulation is revised to fulfil a desired force tracking task after impact. A system of three manipulators mounted on a space free-flyer is simulated, and the results show that, even in the occurrence of an impact due to collision with an obstacle, the response of the MIC algorithm is smooth. Also, relying on the new modification of the algorithm, the contact force follows successfully a desired tracking trajectory.

Impedance control was formulated originally to impose a desired behavior on a single manipulator interacting with its environment. In this paper, a new algorithm called multiple impedance control (MIC) is proposed for the cooperative manipulation of a common object. The general formulation for the MIC algorithm is developed and it is shown that under the MIC law all cooperating manipulators, and the manipulated object exhibit the same designated impedance behavior. At the same time, the potentiality large object inertia and other forces are taken into account. An estimation procedure for contact force determination is given which results in a good approximation even during an impact. Using an example, the response of the MIC algorithm is compared to that of the object impedance control. It is shown that in the presence of flexibility, the MIC algorithm results in an improved performance.

Multiple impedance control (MIC) is a new algorithm which enforces a designated impedance on both a manipulated object, and all cooperating manipulators. In this paper, the MIC is applied to a space robotic system in which robotic arms, mounted on a free-flying-base, manipulate an object. The general formulation of the MIC is extended to include the dynamic coupling between the arms and the base. It is shown that under the MIC law, all participating manipulators, the free-flyer base, and the manipulated object exhibit the same designated impedance behavior. This guarantees good tracking of system manipulators and the object, in performing a manipulation task. A system of two cooperating two-link manipulators is simulated, in which a remote centre compliance is attached to the second end-effector. The object is grabbed with a pivoted grasp condition, i.e. both the translational and rotational motions of the object have to be controlled by end-effector forces. As simulation results show, the response of the MIC algorithm is smooth, even in the occurrence of an impact due to collision with an obstacle.

Transpose Jacobian control is one of the simplest algorithms used in manipulator control. However, since it is not dynamics-based, poor performance may occur in applications where high speed tracking is required. In this paper, a modified transpose Jacobian algorithm is presented and applied to control of space free-flyers. This new algorithm employs stored data of the control command in the previous time step, resulting in improved performance. The gains of the modified algorithm do not need to be large, hence the noise rejection characteristics of the algorithm are improved. Stability analysis, based on Lyapunov's theorems, shows that both the standard and the modified transpose Jacobian algorithms are asymptotically stable. Simulations of both terrestrial and space applications show that the tracking performance of this new algorithm is comparable to that of computed torque algorithms, although it does not require a priori knowledge of plant dynamics.

Studies the motion control of a multi-arm free flying space robot chasing a passive object in close proximity. Free-flyer kinematics are developed using a minimum set of body-fixed barycentric vectors. Using a general and a quasi-coordinate Lagrangian formulation, two dynamics models are derived. Control algorithms are developed that allow coordinated tracking control of the manipulators and the spacecraft. The performance of model-based algorithms is compared, by simulation, to that of a transposed Jacobian algorithm. Results show that the latter can give reasonably good performance with reduced computational burden.>