In this article, we propose a robust hierarchical inverse dynamics control scheme for redundant manipulators, which guarantees both predefined-time convergence of regulation tasks and robustness against model uncertainties/disturbances. Predefined-time convergence of a robotic task means that the task error is regulated to the origin at a desired preset time, independently of the initial state of the robot. The strict hierarchy of tasks is ensured by the so-called dynamic consistency, which avoids conflicts between decoupled task constraints. Thus, it enables the robot with more dexterity for reaching targets in its workspace while overcoming obstacles and joint limits. Predefined-time convergence facilitates the design of a time schedule to execute sequential and simultaneous tasks. All these features are supported by a stability analysis and experiments with two torque-controlled mobile manipulators in pick-and-place applications.

This paper presents a robot trajectory optimization formulation that builds upon numerical optimal control and Lie group methods. In particular, the inherent sparsity of direct collocation is carefully analyzed to dramatically reduce the number of floating-point operations to get first-order information of the problem. We describe how sparsity exploitation is employed with both numerical and analytical differentiation. Furthermore, the use of geometric algorithms based on Lie groups and their associated Lie algebras allow to analytically evaluate the state equations and their derivatives with efficient recursive algorithms. We demonstrate the scalability of the proposed formulation with three different articulated robots, such as a finger, a mobile manipulator and a humanoid composed of five, eight and more than twenty degrees of freedom, respectively. The performance of our implementation in C++ is also validated and compared against a state-of-the-art general purpose numerical optimal control solver.

This paper focuses on important implementation issues of numerical optimal control that are often overlooked. In particular, transcription methods should be carefully implemented for obtaining a discrete representation of the problem. For this purpose, we explain the algorithms to solve the minimum-effort problem by applying a direct collocation method based on B-Splines. In addition, we describe how to compute the gradient of the objective function as well as the Jacobian of the constraints without the use of finite differences and automatic differentiation. Geometric algorithms based on Lie groups and Lie algebra are examined to efficiently compute the analytical derivatives of the equations of motion of articulated robots. These ingredients allow the fast computation of dynamically feasible robot motions. We provide numerical comparisons with a biped robot to validate our recipe against classical direct collocation methods.

This paper proposes a general scheme based on terminal attractors to parametrize operational tasks with respect to time in continuous kinematic controllers. Commonly, a pseudo-inverse operator is applied to solve operational tasks. However, it is known that discontinuities in the control signals appear as a by-product of task transitions during motion execution. In particular, these transitions involve the insertion, removal and swapping of tasks. Recently, some methods have been reported that overcome such discontinuities in the control signals. In this work, we provide time parametrization capabilities to these continuous kinematic controllers in order to handle the time axis of operational tasks at will. Then, we show that the proposed scheme can be naturally extended for the case of prioritized kinematic tasks while preserving continuity under task transitions. Our scheme is validated in a real experiment with a NAO humanoid robot.

A passivity-based model-free control scheme for an underwater fully actuated vehicle-manipulator system (UVMS) in contact tasks is proposed. Orthogonalized motion and force second-order sliding modes are enforced for all time for the redundant noninertial robotic UVMS, including when it is subject to a class of fluid disturbances. To this end, we first determine the constrained dynamics using the quasi-Lagrangian formulation to explicitly characterize hydrodynamic fluid perturbations. Our scheme aims at exploiting the structural properties of Lagrangian systems, then we derive a mapping between the quasi-Lagrangian UVMS to its equivalent Lagrangian form, and study the conditions for open-loop passivity preservation during the interaction of postures and contact constraints between the end effector of the UVMS and the rigid contact surface of bulky objects in cluttered submarine environments. Internal motions are simultaneously computed by solving, in the tangent subspace of the contact manifold, a hierarchy of secondary tasks to satisfy the posture constraints. More importantly, the solution shapes the extended errors that are used to preserve passivity and to enforce dissipativity so as to guarantee local exponential stability without any knowledge of the complex UVMS dynamics, and the energetic performance of the UVMS in closed-loop. Illustrative simulations are discussed to show the feasibility of the proposed scheme.

Classical prioritized inverse kinematics (PIK) allows to generate admissible trajectories for redundant robotic systems according to a prioritized finite set of kinematic tasks to simultaneously handle multiple posture constraints. In this paper, we propose a novel regulation scheme that permits to define terminal attractors (TA) at each priority level for satisfying an additional constraint which is the final time. TA were first introduced in the context of movement neuroscience for studying the targeting problem in reaching movements. Based on the underlying properties of TA, we extend PIK methods for achieving desired time convergence of each task while guaranteeing smooth transitions between active and inactive tasks during execution. The proposed scheme is illustrated in simulation with branched robotic manipulators and verified with a real redundant robotic arm.

We propose a scheme to deal simultaneously with local motion planning and dynamic control of redundant cooperative robots subject to holonomic, posture and loop-closure constraints. In contrast to previous contributions, an iterative method, that glue together the problem of kinematic motion planning with dynamic control, generates the sequence of feasible collision-free motions by combining in a single strategy the task-priority redundancy formalism with a joint model-free smooth force-motion control scheme based on a well-posed projection, which allows motions of the system only in the tangent subspace of the contact constrained manifold. Overall the new algorithm is able to compute fast and accurately local solutions involving severely constrained robotic motions. We have successfully verified in simulations the effectiveness of the proposed iterative method in the context of cooperative manipulation tasks.

The paper in question [G. Arechavaleta, J. P. Laumond, H. Hicheur, and A. Berthoz, “An optimality principle governing human walking,” IEEE Trans. Robot., vol. 24, no. 1, pp. 5-14, Feb. 2008] suggested that human-walking paths minimize variation in curvature and hence can be approximated by the solution to an optimal control problem. This conclusion was reached by analysis of experimental data based on the maximum principle. We correct two errors in this analysis and consider their consequences.

In this paper, we investigate different possible strategies underlying the formation of human locomotor trajectories in goal-directed walking. Seven subjects were asked to walk within a motion capture facility from a fixed starting point and direction, and to cross over distant porches for which both position and direction in the room were changed over trials. Stereotyped trajectories were observed in the different subjects. The underlying idea to attack this question has been to relate this problem to an optimal control scheme: the trajectory is chosen according to some optimization principle. This is our basic starting assumption. The subject being viewed as a controlled system, we tried to identify several criteria that could be optimized. Is it the time to perform the trajectory? The length of the path? The minimum jerk along the path? We found that the variation (time derivative) of the curvature of the locomotor paths is minimized. Moreover, we show that the human locomotor trajectories are well approximated by the geodesics of a differential system minimizing the norm of the control. Such geodesics are made of arcs of clothoids. The clothoid or Cornu spiral is a curve, whose curvature grows with the distance from the origin.

This paper presents an approach to automatically compute animations for virtual (human-like and robot) characters cooperating to move bulky objects in cluttered environments. The main challenge is to deal with 3D collision avoidance while preserving the believability of the agent's 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 independently, and finally to automatically tune the animation to avoid residual collisions. These three steps are applied consecutively to synthesize an animation. The different techniques used, such as probabilistic path planning, locomotion controllers, inverse kinematics and path planning for closed kinematic chains are explained, and the way to integrate them into a single scheme is described.

This paper presents a motion planner for a digital mannequin carrying objects in cluttered environments. The goal is to account for 3-dimensional obstacle avoidance, eye-convincing locomotion as well as manipulation constraints within an integrated motion planning approach. This approach combines probabilistic path planning methods, a motion capture based walking controller and inverse kinematics techniques.