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This paper presents a new geometric algorithm to efficiently compute the analytical differentiation of the Articulated-body Algorithm (ABA) with respect to the state variables. Despite the fact that ABA solves the forward dynamics problem in linear-time for branched-multibody systems, its explicit differentiation is not straightforward, and computationally demanding tensor products and contractions appear. The proposed algorithm makes use of Lie algebraic and multilinear operations to recursively exploit the underlying sparsity of the linearization problem. As a result, the arithmetic complexity is dramatically reduced without affecting the analytical solution. Since the linealization of forward dynamics is of great importance in robot trajectory optimization, a differential dynamic programming solver is employed to demonstrate the performance of our algorithm with humanoid robot models such as N{\footnotesize AO} and HRP-2. In addition, we provide the computational cost with different robots using an optimized C++ implementation that can be found at https://github.com/garechav/geombd_crtp.git}{https://github.com/garechav/geombd\_crtp.

In this paper, we propose a state-feedback controller that is capable to achieve predefined-time convergence for a class of nonlinear second order systems that can be linearized to a perturbed double integrator. The controller relies on the use of time base generators. Also, we study the link between the proposed predefined-time controller and the widely applied task-based inverse dynamics framework to control kinematically redundant robots. We show that positioning tasks assigned to the robot subject to joint-limits constraints are successfully completed in a user defined time regardless of the robot’s initial state. Moreover, the proposed task-based controller is robust to parametric uncertainties and matched disturbances since it includes a term given by a super-twisting control. This is verified through simulations with a kinematically redundant mobile-manipulator KUKA youBot with eight degrees of freedom.

This paper presents an optimization-based control scheme for generating online multi-vehicle coordination behaviors to accomplish missions in indoor environments. The proposed control scheme relies on the use of hierarchical task functions in terms of the multi-vehicle configuration variables. The task functions are related to individual and group obstacle avoidance, reaching fixed targets, group trajectory tracking, maintaining formations, enclosing the group within a geometric area, among others. The stack of hierarchical tasks automatically handles possible conflicts between them. Quadratic programs are formulated for explicitly solving inequality and equality task constraints at any hierarchy. In addition, a finite state machine is employed to build complex group behaviors for successfully fulfilling group missions. The proposed control scheme is demonstrated on two experiments with static and moving obstacles where a group composed by six vehicles tracks a predefined trajectory for the center of mass of the group. In the second experiment, the group is asked to clean the workspace by pushing movable objects.

Human locomotion was investigated in a goal-oriented task where subjects had to walk to and through a doorway starting from a fixed position and orientation in space. The door was located at different positions and orientations in space, resulting in a total of 40 targets. While no specific constraint was provided to subjects in terms of the path they were to follow or the expected walking speeds, all of them generated very similar trajectories in terms of both path geometry and velocity profiles. These results are reminiscent of the stereotyped properties of the hand trajectories observed in arm reaching movements in studies over the last 20 years. This observation supports the hypothesis that common constraining mechanisms govern the generation of segmental and whole-body trajectories. In contrast, we observed that the subjects placed their feet at different spatial positions across repetitions, making unlikely the hypothesis that goal-oriented locomotion is planned as a succession of steps. Rather, our results suggest that common planning and/or control strategies underlie the formation of the whole locomotor trajectory during a spatially oriented task.

Despite the theoretically infinite number of possible trajectories a human may take to reach a distant doorway, we observed that locomotor trajectories corresponding to this task were actually stereotyped, both at the geometric and the kinematic levels. In this paper, we propose a computational model for the formation of human locomotor trajectories. Our model is adapted from smoothness maximization models that have been studied in the context of hand trajectory generation. The trajectories predicted by our model are very similar to the experimentally recorded ones. We discuss the theoretical implications of this result in the context of movement planning and control in humans. In particular, this result supports the hypothesis that common principles, such as smoothness maximization, may govern the generation of very different types of movements (in this case, hand movements and whole-body movements).

In this work, we propose a landmark-based navigation approach that integrates (1) high-level motion planning capabilities that take into account the landmarks position and visibility and (2) a stack of feasible visual servoing tasks based on footprints to follow. The path planner computes a collision-free path that considers sensory, geometric, and kinematic constraints that are specific to humanoid robots. Based on recent results in movement neuroscience that suggest that most humans exhibit nonholonomic constraints when walking in open spaces, the humanoid steering behavior is modeled as a differential-drive wheeled robot (DDR). The obtained paths are made of geometric primitives that are the shortest in distance in free spaces. The footprints around the path and the positions of the landmarks to which the gaze must be directed are used within a stack-of-tasks (SoT) framework to compute the whole-body motion of the humanoid. We provide some experiments that verify the effectiveness of the proposed strategy on the HRP-2 platform.

We propose a simple and efficient online strategy based on inertial sensors to follow human arm movements in the task space by robotic platforms. The strategy is composed by the following ingredients: 2 inertial sensors attached to the human arm and forearm, the differential kinematics (DK) as well as the dynamic model of the corresponding robot and a motion control scheme. We use inertial sensors to obtain the orientation measurements of the human bodies in real-time. These body parameters together with the DK module allow us to map human hand trajectories into the joint space of the robot, where a standard PID control is implemented. Overall our strategy is able to transfer motion skills from human to a given robot by means of an online inertial sensor-guided motion control. Moreover, our method can be used for robot teleoperation applications in a master-slave configuration, with a human interface based on inertial sensors. We have successfully validated in simulations the effectiveness of the proposed strategy in a 2 degrees of freedom (dof) planar robot.

Human locomotion was investigated in a goal-oriented task where subjects had to walk to and through a doorway starting from a fixed position and orientation in space. The door was located at different positions and orientations in space, resulting in a total of 40 targets. While no specific constraint was provided to subjects in terms of the path they were to follow or the expected walking speeds, all of them generated very similar trajectories in terms of both path geometry and velocity profiles. These results are reminiscent of the stereotyped properties of the hand trajectories observed in arm reaching movements in studies over the last 20 years. This observation supports the hypothesis that common constraining mechanisms govern the generation of segmental and whole-body trajectories. In contrast, we observed that the subjects placed their feet at different spatial positions across repetitions, making unlikely the hypothesis that goal-oriented locomotion is planned as a succession of steps. Rather, our results suggest that common planning and/or control strategies underlie the formation of the whole locomotor trajectory during a spatially oriented task.

This paper deals with mechanical part assembly planning. The goal is to automatically compute a collision-free path for both the part to be assembled and the mannequin manipulating it. Two approaches are proposed according to the difficulty of the problem. Both are based on a general probabilistic diffusion algorithm working in the configuration space of the considered system. The first approach consists in first planning a path for the part alone and then in checking the feasibility of the solution by adding the mannequin. The second one considers the part grasped and the mannequin as a single system. While the first approach performs quickly the second one is able to solve more constrained and difficult cases. Both solutions are based on the same path planning library allowing the user to easily evaluate the proposed solutions. Experimental results based on feedback experiences in automotive industry are presented

This paper presents a motion planner to automatically compute animations for virtual (human, humanoid or robot) mannequins cooperating to move bulky objects in cluttered environments. The main challenge is to deal with 3D collision avoidance while preserving the believability of the agents behaviors. To accomplish the coordinated task, a geometric and kinematic decoupling of the system is proposed. This decomposition enables us to plan a collision-free path for a reduced system, then to animate locomotion and grasping behaviors in parallel, and finally to clean up the animation from residual collisions. These three steps are automatically applied making use of different techniques such as probabilistic path planning, locomotion controllers, inverse kinematics and path planning for closed-kinematic mechanisms.

This work presents a differential system which accurately describes the geometry of human locomotor trajectories of humans walking on the ground level, in absence of obstacles. Our approach emphasizes the close relationship between the shape of the locomotor paths in goal-directed movements and the simplified kinematic model of a wheeled mobile robot. This kind of system has been extensively studied in robotics community. From a kinematic perspective, the characteristic of this wheeled robot is the nonholonomic constraint of the wheels on the floor, which forces the vehicle to move tangentially to its main axis. Humans do not walk sideways. This obvious observation indicates that some constraints (mechanical, anatomical...) act on human bodies restricting the way humans generate locomotor trajectories. To model this, we propose a differential system that respects nonholonomic constraints. We validate this model by comparing simulated trajectories with actual (recorded) trajectories produced during goal-oriented locomotion in humans. Subjects had to start from a pre-defined position and direction to cross over a distant porch (position and orientation of the porch were the two manipulated factors). Such comparative analysis is undertaken by making use of numerical methods to compute the control inputs from actual trajectories. Three body frames have been considered: head, pelvis and trunk. It appears that the trunk can be considered as a kind of a steering wheel that steers the human body with a delay of around 0.2 second. This model has been validated on a database of 1,560 trajectories recorded from seven subjects. It opens a promising route to better understand the human locomotion via differential geometry tools successfully experienced in mobile robotics

"This master thesis work presents the theoretical fundamentals, development strategies and implementation results of a walking pattern generator for humanoid robots, which is suitable for visually-guided tasks. In first place, a general introduction about the state-of-the-art related to research on humanoid locomotion solutions is introduced, as well as a general overview about humanoid robots, making emphasis on the main characteristics that identify this type of robots from the rest of the existing platforms. Furthermore, a method to construct the kinematic model for robots based on a tree-like structure is proposed. Subsequently, several algorithms and relations necessary to compute the model forward kinematics and to calculate the different versions of Jacobian matrices are introduced. Moreover, this work presents and explains two powerful techniques to compute the model inverse kinematics. These methods take advantage of the inherent redundancy of humanoid robots to simultaneously solve a determined amount of kinematic tasks, based on a prioritized scheme. Later, all important fundamentals related to the humanoid dynamics are introduced. Particularly, the concept of the Zero-Moment Point (ZMP), which is a key parameter on humanoid locomotion, is presented in this thesis work and besides, some methods to determine the position of this parameter are discussed as well. This thesis also presents some schemes to model the process of biped locomotion, focusing on a method to determine the optimal trajectory of the robot Center of Mass (CoM), based on the preview control of the reference ZMP position. Besides, all fields that are studied in this thesis are taken together into a global architecture for walking pattern generation, consisting on two stages of control, each of them containing the processes of linear-quadratic regulation of the reference ZMP, Prioritized Inverse Kinematics (PIK) and approximation of the real position of the ZMP based on the robot movements. A genuine verification of the functionality of the designed walking pattern generator is exposed at the end of this thesis work, by presenting the results of the performed simulations on a virtual humanoid model, as well as the experimentations on a physical humanoid robot."