Cable-Driven Parallel Robots (CDPRs) have shown significant potential in industrial applications due to their large workspace, high payload capacity, and flexibility. Nonetheless, ensuring safe and efficient human-robot collaboration, particularly during carrying tasks, remains an open problem. This paper primarily contributes a cable tension–based metric for detecting contact events, combined with a frequency-domain analysis of estimated external wrenches to distinguish different contact scenarios. Building upon this framework, three common contact scenarios are then addressed: (i) payload placement and removal without rigid attachment to the moving-platform (SC1), (ii) unintentional human-cable collisions (SC2), and (iii) human-platform collisions (SC3). Specific management strategies are then proposed, including real-time mass estimation for payload handling, cable tension release for human-cable collisions, and a compliant trajectory controller for human-platform collisions. Experimental validations on a CDPR prototype demonstrate accurate scenario classification and safe contact handling without compromising overall productivity. By facilitating safer interactions, improved adaptability, and reliable handling of diverse contact events, this work expands the applicability of collaborative CDPRs in real-world industrial and logistic settings.

International audience

This paper proposes a new kind of light-weight manipulators suitable for safe interactions. The proposed manipulators use anti-parallelogram joints in series, referred to as X-joints. Each X-joint is remotely actuated with cables and springs in parallel, thus realizing a tensegrity one-degree-of-freedom mechanism. As compared to manipulators built with simple revolute joints in series, manipulators with tensegrity X-joint offer a number of advantages, such as an intrinsic stability, variable stiffness and lower inertia. This new design was inspired by the musculosleketon architecture of the bird neck that is known to have remarkable features such as a high dexterity. The paper analyzes in detail the kinetostatics of a X-joint and proposes a 3-degree-of-freedom manipulator made of three such joints in series. Both simulation results and experiment results conducted on a test-bed prototype are presented and discussed.

Actual control of most humanoid robots is based on the 3D linear inverted pendulum and assumes an horizontal displacement of the center of mass of the robot while obviously the center of mass in human walking is characterized by vertical oscillations. The objective of the paper is to show that these oscillations have a crucial role for the high level control of the walk. Based on a controlled length inverted pendulum model of the walker, it will be shown that vertical oscillations induce a self stabilization of the walk while this self stabilization is not observed in the case of a horizontal motion of the center of mass. The results are essentially based on the evolution of the angular momentum throughout the walk. The decrease of the angular momentum during the change of support is determinant to introduce a dependence between the path of the center of mass and the walking velocity. For a large set of walking characteristics (stride, velocity ...) a self synchronization of the motion in the sagittal and frontal planes appears that allows a low level control to produce stable cyclic gaits.

International audience

A second order sliding mode controller is utilised to track reference trajectories for all the joints of a fully actuated biped robot. The existing tuning rules for the `twisting' controller are used to guarantee a priori attainment of a prescribed settling time between two successive impacts. The joint torque is modeled as the control input. Smoothing of the discontinuous controller is carried out by introducing a high gain linear controller inside a boundary layer defined by an arbitrarily small region around the origin thereby avoiding numerical errors in the simulations. The overall accuracy of motion control is dictated by the size of this layer leading to practical stability of the closed-loop system. The main contribution of the paper is to provide straightforward and realizable engineering guidelines for the reference trajectory generation and for the tuning of a robust finite time controller for achieving stable gait of a biped in the presence of disturbances in both continuous and impact phases. Numerical simulations of a biped robot are shown to support the theoretical results.

Bio-inspired by moth or humming-birds, several micro air vehicles (MAV) have recently been developed. In these systems, the motion of the lifting surface is complex and modeled by flapping motion-controlled soft wings. The synchronization of the actuated periodic flapping motion of the wings and that of passive twisting degrees of freedom (dof) allows producing hovering flight. Depending on the feature of the MAV such as stiffness, and geometric characteristic, hovering flight can be naturally stable or not. In the first case hovering is obtained via an open loop control (or a local closed loop control) while in the second case a global control strategy is required to achieve the same objectives. Thus, it is crucial to take into account the influence of the design of the MAV on the control in order to choose an appropriate morphology that can reduce the burden of control. In this paper mathematical tools and methodologies are proposed to achieve this objective and reduce the computational cost of control.

Some fish species use electric sense to navigate efficiently in the turbid waters of confined spaces. This paper presents a first attempt to use this sense to control a group of nonholonomic rigid underwater vehicles navigating in a cooperative way. A leader whose motion is unknown to the others serves as an active agent for its passive neighbor, which perceives the leader's electric field via current measurements and moves in order to follow a trajectory relative to it. Then, this passive agent, becomes in its turn the leader for the next agent and so on. Sufficient conditions of convergence of the control law are derived for electric current servoing. This is achieved without the explicit knowledge of the location of the agents. Some limits on the possible motion of the leader along with the importance of the choice of controlled outputs are demonstrated. Switching between different group configurations by following a virtual agent is also described. Simulation and experimental results illustrate the theoretical study.

Thanks to an electro-sensible skin, some species of fish can feel the surrounding electric field generated by them-self or other fish. Known under the name of “electric-sense”, this ability allows these fish to navigate in confined surroundings. Based on a bio-inspired electric sensor, this article presents how this electric sense can be used for the navigation in formation of several underwater vehicles. The formation considered is a file, each vehicle is assumed to follow its predecessor at a given distance. In confined environment, the file formation is interesting since fish can follow the same safe path. Being based on the servoing of the electric measurements, these laws do not require the knowledge of the location of the agents. The underwater vehicle studied have non holonomic properties, their forward velocity has no lateral component. Depending on the choice of the controlled outputs (combination of electric measures) we will see that path followed by the follower agents can be different and a methodology to choose the output will be defined in order that all the agents follow the leader path in presence of curved motion of the leader. The influence of the number of electrodes is discussed. Simulation results illustrate the proposed approach.

This paper shows how a sensor inspired by an electric fish could be used to help navigate in confined environments. Exploiting the morphology of the sensor, the physics of electric interactions, as well as taking inspiration from passive electrolocation in real fish, a set of reactive control laws encoding simple behaviors, such as avoiding any electrically contrasted object, or seeking a set of objects while avoiding others according to their electric properties, is proposed. These reflex behaviors are illustrated on simulations and experiments carried out on a setup dedicated to the study of electric sense. The approach does not require a model of the environment and is quite cheap to implement.

Thanks to an electro-sensible skin, some species of fish can feel the perturbations of a self generated electric field caused by their surroundings variations. Known under the name of “electric-sense”, this ability allows these fish to communicate and navigate in confined surroundings wetted by turbid waters where vision and sonar cannot work. Based on a bio-inspired electric sensor recently proposed in [1], this article presents a first attempt to use electric sense for the navigation in formation of a set of rigid underwater vehicles. The navigation strategy combines some behaviours observed in electric fish as well as a follower-leader strategy well known from multi-robot navigation. Being based one the servoing of the electric measurements, these laws do not require the knowledge of the location of the agents. Sufficient convergence conditions of the resulting control laws are given. Moreover, some limits on the possible motion of the leader are exhibited and the importance of the choice of controlled outputs is discussed too. Finally, simulation results illustrate the feasibility of the approach.

Energetic efficiency and stability are the fundamental criteria which can improve the autonomy and task performance capabilities of humanoid robots. The scope of this paper is to investigate the energetic effects of knee locking and addition of torsional springs to different joints of a seven-link fully actuated planar bipedal robot. The focus is on the reduction of energy consumption during walking. The energetic cost of walking is determined without joint stiffness and knee locking as a baseline for the comparison of results. In the first approach, the gait trajectory is optimized by adding springs to different joints and energetic cost of walk is then calculated at different walking speeds. The second approach presented in this paper is to mechanically lock the support knee and then optimize the gait and calculate the walking cost. The energetic cost of walking determined for the above two cases is then compared to the baseline cost. It is observed that addition of torsional springs at both hips reduce the walking cost up to 50%, support hip up to 85% with spring stiffness as an optimization variable for both cases while mechanically locking the support knee reduces the cost of walking up to 25% with gait and knee locking angle optimized.

This article proposes a solution to the problem of the navigation of underwater robots in confined unstructured environments wetted by turbid waters. The solution is based on a new sensor bio-inspired from electric fish. Exploiting the morphology of the sensor as well as taking inspiration from passive electro-location in real fish, the solution turns out to be a sensory-motor loop encoding a simple behavior relevant to exploration missions. This behavior consists in seeking conductive objects while avoiding insulating ones. The solution is illustrated on experiments. It is robust and works even in very unstructured scenes. It does not require any model and is quite cheap to implement.

Electric fish feel the perturbations of a self-generated electric field through their electro-receptive skin. This sense allows them to navigate and reconstruct their environment in conditions where vision and sonar cannot work. In this article, we use a sensor bio-inspired from this active sense to address the problem of small objects reconstruction and electrolocation. Based on a Kalman filter, any small object in the surrounding of the motion controlled sensor can be encapsulated into an equivalent sphere whose location is well estimated by the filter. Experimental results illustrate the feasibility of the approach.

Pages 3700 -- 3705

This paper focuses on steering a 3D robot while walking on a flat surface. A hybrid feedback controller designed in for stable walking along a straight line is modified so that it is capable of adjusting the net yaw rotation of the robot over a step in order to steer the robot along paths with mild curvature. The controller is designed on the basis of a single pre-defined trajectory for periodic walking along a straight line. In order to illustrate the role of internal/external (i.e., medial/lateral) rotation at the hip in achieving curved walking motions, the performance of two robots, one with internal/external rotation and one without, is compared.

The aim of this paper is to perform the navigation of an underwater robot equipped with a sensor using the electric sense. The robot navigates in an unbounded environment in presence of spheres. This sensor is inspired of some species of electric fish. A model of this sensor composed of n spherical electrodes is established. The variations of the current due to the presence of the sphere is related to the model of Rasnow. Unscented Kalman Filter is used to localize the robot with respect to the sphere and to estimate the size of the sphere. We show that bio-inspired motions improve the detection of the spheres. We illustrate the efficiency of the method in two cases: a two electrodes sensor and a four electrodes sensor.

This paper studies the effect of controlled outputs selection on the walking stability for an under-actuated planar biped robot. The control is based on tracking reference motions expressed as function of time. First, the reference motions are adapted at each step in order to create an hybrid zero dynamic system. Second, the stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincaré map of the hybrid zero dynamics. It shows that for the same robot, and for the same reference trajectory, the stability of the walking can be modified by some pertinent choices of controlled outputs. Third, we find that, at the desired moment of impact for one step, the height of swing foot is nearly zero for all the stable walking, though the configurations of the robot are not the desired configurations. Based on this, we propose a new method to choose the controlled outputs to obtain the stable walking for robot. As a result, two stable domains for the controlled outputs selection are obtained. Furthermore, we point out that, this kind of control law, which based on reference motion as a function of time, can produce better convergent property than that based on reference motion as a function of a state of robot via pertinent choices of controlled outputs.

This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3-D bipedal robot consisting of a torso, revolute knees, and passive (unactuated) point feet. The walking surface is assumed to be rigid and flat; the contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and six actuators. In addition to the reduced number of actuators, the interest of studying robots with point feet is that the feedback control solution must explicitly account for the robot's natural dynamics in order to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics (HZD), a very successful method for planar bipeds, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit, for a 3-D (spatial) bipedal walking robot. This method allows the computations for the controller design and the periodic orbit to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincare map of the HZD. Most periodic walking gaits for this robot are unstable when the controlled outputs are selected to be the actuated coordinates. Three strategies are explored to produce stable walking. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an event-based controller to modify the eigenvalues of the (linearized) Poincare map. In the third approach, the effect of output selection on the zero dynamics is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller.

Fast human walking includes a phase where the stance heel rises from the ground and the stance foot rotates about the stance toe. This phase where the biped becomes underactuated is not present during the walk of humanoid robots. The objective of this study is to determine if the introduction of this phase for a 3D biped robot is useful to reduce the energy consumed in the walking. In order to study the efficiency of this new gait, two cyclic gaits are presented. The first cyclic motion is composed of successive single support phases with flat stance foot on the ground. The second cyclic motion includes a sub-phase of rotation of the supporting foot about the toe. For these two gaits, optimal motions are designed by minimizing a functional torques cost. It is shown that for fast motion a foot rotation sub-phase is useful to reduce the functional cost.

Consider a biped evolving in the sagittal plane. The unexpected rotation of the supporting foot can be avoided by controlling the zero moment point (ZMP). The objective of this study is to propose and analyze a control strategy for simultaneously regulating the position of the ZMP and the joints of the robot. If the tracking requirements were posed in the time domain, the problem would be underactuated in the sense that the number of inputs would be less than the number of outputs. To get around this issue, the proposed controller is based on a path-following control strategy, previously developed for dealing with the underactuation present in planar robots without actuated ankles. In particular, the control law is defined in such a way that only the kinematic evolution of the robot's state is regulated, but not its temporal evolution. The asymptotic temporal evolution of the robot is completely defined through a one degree-of-freedom subsystem of the closed-loop model. Since the ZMP is controlled, bipedal walking that includes a prescribed rotation of the foot about the toe can also be considered. Simple analytical conditions are deduced that guarantee the existence of a periodic motion and the convergence toward this motion.

Consider a biped evolving in the sagittal plane. The unexpected rotation of the supporting foot can be avoided by controlling the zero moment point or ZMP. The objective of this study is to propose and analyze a control strategy for simultaneously regulating the position of the ZMP and the joints of the robot. If the tracking requirements were posed in the time domain, the problem would be underactuated in the sense that the number of inputs would be less than the number of outputs. To get around this issue, the proposed controller is based on a path-following control strategy previously developed for dealing with the underactuation present in planar robots without actuated ankles. In particular, the control law is defined in such a way that only the kinematic evolution of the robot's state is regulated, but not its temporal evolution. The asymptotic temporal evolution of the robot is completely defined through a one degree of freedom subsystem of the closed-loop model. Simple analytical conditions, which guarantee the existence of a periodic motion and the convergence towards this motion, are deduced.

This paper investigates the energetic effects of adding springs at the passive ankles of a planar five-link, four-actuator walking biped robot. The energetic cost of walking with springs was determined by using a walking motion designed for the biped without springs added. The walking motion was then optimized for the presence of springs of various arbitrarily chosen stiffnesses and offset angles. The stability properties of the motions that resulted were checked. The energetic costs of walking and standing were then computed. It was found that standing with springs was more efficient, while walking was more costly than the same action without springs. Finally, the spring characteristics (stiffness and offset angle) and the motion were optimized simultaneously. The costs for walking and standing were computed, revealing that walking with springs was more efficient and standing was more costly than doing either without springs. A methodical approach to choosing the size of the feet based on this analysis of the spring characteristics is also presented.

This study proposes the analysis of two control strategies for a planar biped. One control makes it possible to find and study the existence of a cyclic motion and its stability, in this approach the avoidance of unexpected rotation of the supporting foot is treated via the control of the center of pressure or CoP. When the task is a simultaneous control of the joints and of the CoP, the system becomes under-actuated in the sense that we have fewer inputs than outputs. This control law is designed to track a desired geometric evolution of the biped configuration, and not the temporal evolution. But the temporal evolution is completely defined and can be analyzed through the study of a model with one degree of freedom. The influence of the desired geometric evolution of CoP on the stability properties of the control law is studied. The second control law improve the performances of the first one by increasing the rate of convergence towards the cyclic motion and enlarging the basin of attraction of the control. This improvement of the performances is possible by forcing the convergence by the control and relaxing the CoP evolution to be within the foot limits

The objective of this study is to obtain optimal cyclic gaits for a biped without actuated ankle. For the walking, the gait is composed of successive single support phases and instantaneous double support phases that are modeled by passive impact equations. The legs swap their roles from one single support phase to the next one. During each phase the evolution of the joints variables is assumed to be polynomial functions of a scalar path parameter. The coefficients of the polynomial functions are chosen to optimise a torque criterion and to insure a cyclic motion for the biped. Furthermore, the optimal gait is defined with respect to given performances of actuators. The torques and velocities at the output of the gearbox are bounded. For this study, the physical parameters of a prototype are used. Initial starting motions that are composed of a double support and a transitional single support are also defined.

The objective of this study is to analyze the stability of control strategy for a planar biped robot. The avoidance of unexpected rotation of the supporting foot is treated via the control of the zero moment point or ZMP. When the task is a simultaneous control of the joints and of the ZMP, the system becomes under-actuated in the sense that there is less inputs than the number of outputs. The control law is defined in such a way that only the geometric evolution of the biped configuration is controlled, but not the temporal evolution. The temporal evolution during the geometric tracking is completely defined and can be analyzed through the study of a model with one degree of freedom. Simple conditions, which guarantee the existence of a cyclic motion and the convergence towards this motion, are deduced.

Numerous robotic tasks associated with underactuation have been studied in the literature. For a large number of these in the plane, the mechanical models have a cyclic variable, the cyclic variable is unactuated, and all shape variables are independently actuated. This paper formulates and solves two control problems for this class of models. If the generalized momentum conjugate to the cyclic variable is conserved, a set of that outputs is defined. If the generalized momentum conjugate to the cyclic variable is not conserved, a feedback that asymptotically stabilizes an equilibrium is given. The results are illustrated on a ballistic nip motion and on a balancing task.

This paper presents a control law for the tracking of a cyclic reference trajectory by an underactuated biped robot. The robot studied is a five-link planar robot. The degree of underactuation is one during the single support phase. The control law is defined in such a way that only the geometric evolution of the robot is controlled, not the temporal evolution. To achieve this objective, we consider a time-scaling control. For a given reference path, the temporal evolution during the geometric tracking is completely defined and can be analyzed through the study of the dynamic model. A simple analytical condition is deduced that guarantees convergence toward the cyclic reference trajectory. This condition implies temporal convergence after the geometric convergence. This condition is defined on the cyclic reference path. The control law is stable if the angular momentum around the contact point is greater at the end of the single support phase than at the beginning of the single support phase.

Several French laboratories, joint in the CNRS Project "Control of Legged Robots", have defined a biped robot intended to experiment walking and running gaits. This biped is made of one trunk and two legs without feet, animated by means of four active articulations. This paper describes the design of the prototype, closely combining technological considerations and dynamics ones. The geometrical parameters and actuation characteristics are defined with the aim of generating walking and running gaits with rather large velocities. Each gait is synthesised with optimization criterion including the energy consideration with respect to actuator performances. During the single support phase and the flight phase, the biped is under-actuated. The synthesis of the corresponding trajectories is carried out by means of a local optimization method, and the cyclic constraints being handled as equality constraints. The optimal gear ratio of the speed reducers is computed.

Exploiting recent results based on differential geometric control theory, it is shown in the paper that, by suitable choice of generalized coordinates, the biped dynamics may be represented by an almost linear model. This representation enables efficient use of the well known classical control methodology to define stable control. This approach is based on a complete 2-DOF and 3-DOF nonlinear model representation of robot dynamics over operative envelope without additional approximation. In this presentation, extensive use of mathematical terminology is avoided and physical interpretations of variables is proposed.

The impulsive torque at the beginning and end of the ballistic motion between these two instants give energetically optimal motion for a pendulum. Many authors assume that in human walking, muscle activities alternate with some periods of relaxation. From these two arguments, we assume that a motion defined by ballistic motion and impulsive control at dual support instances will lead to an energetically economical trajectory. Optimal configurations are defined, and smooth changes on the reference trajectory are proposed to obtain a trajectory which can be followed with finite torques. The physical constraints on the reaction forces to avoid take off or sliding of the biped walking robot, and saturation on the torques produced by the actuators are explicitly taken into account.

The goal of this paper is to define a control law and reference trajectories for a legged robot with feet. We use a computed torque control law associated with a desired motion of the legged robot derived from a ballistic trajectory. This approach leads to the same distribution of the torques as it can be observed for humans, and respects the assumption that muscle activities alternate with some periods of relaxation. Simulations are made on a simple model of quadruped for a dynamically stable planar gait.

In this paper, two methods to calculate the direct dynamic model (DDM) of walking robots are presented. These methods derive from the Walker-Orin (1982) method and from the Featherstone (1983) method, generally used to compute the DDM of robot manipulators. The comparison is made on the number of operations for each method and for walking robots: a biped robot and a quadruped robot. It is shown that Featherstone's method is better than Walker-Orin's one.

At singular configurations, the form taken by the Jacobian matrix let one believe that no motion is possible along particular directions (called singular directions). For some singularities, however, a motion along a singular direction is possible if the timing law is properly chosen. In other cases the constraints on the trajectory are stronger, consequently the tangent to the path at the singular point cannot be arbitrary. In this paper, a classification of singularities is proposed and the set of all feasible trajectories is defined for each type of singularities. Different examples are provided.

A Cartesian control law usually requires the inversion of the Jacobian matrix. In singular configurations, motions along particular directions (degenerate directions) seem to be infeasible. In this paper, the constraints that the reference trajectory must satisfy to be correctly tracked are studied for different types of singularities. For an external singularity, no constraint exists on the path, so a motion along a degenerate direction is possible. For an internal singularity the constraints on the trajectory are stronger, so the tangent to the path at the singular point can not be arbitrary. Then, a method is proposed for computing the control input to obtain a perfect tracking of a given reference trajectory satisfying the constraints described above.>

The authors propose a nonlinear control law defined to minimize the variation of the performances of the robot whatever the location of the trajectory in the workspace. It takes elastic deflections into account, and minimizes the norm of the difference between the real behavior and the desired behavior of the robot. A method for calculating the gain is proposed, and the results are compared with the linear control laws. The applicability domains on both control laws are considered, and robustness is studied.>

An algorithm for the solution of the inverse kinematic problem of the redundant robots is presented. The method has the advantage of generating efficient symbolic solution from the number-of-operations point of view; it gives the null space solution with a computational cost comparable to that of the pseudoinverse solution. The given method can be used to provide most of the optimization criteria used in the literature; an exact solution is proposed for most of them.>

This paper presents an efficient algorithm for the solution of the pseudo inverse kinematic problem of robots. The given inverse kinematic calculationcan be usedatthe singular positions and for redundant robots. The presented method has the advantages of being explicit and that it reduces considerably the number of operations compared to the numerical methods.