Section: New Results

Robotics

Analysis of Cable-driven parallel robots

Participants : Jean-Pierre Merlet [correspondant] , Yves Papegay.

We have continued the analysis of suspended CDPRs for control and design purposes. This analysis is heavily dependent on the behavior of the cable. Three main models can be used: ideal (no deformation of the cable due to the tension, the cable shape is a straight line between the attachments points), elastic (cable length changes according to the tension to which it is submitted, straight line cable shape) and sagging (cable shape is not a line as the cable is submitted to its own mass). The different models leads to very different analysis with a complexity increasing from ideal to sagging. All cables exhibit sagging but the sagging effect is often neglected if the CDPR is relatively small while it definitively cannot be neglected for large CDPRs. The most used sagging model is the Irvine model  [24]. This is a non algebraic planar model with the upper attachment point of the cable is supposed to be grounded: it provides the coordinates of the lowest attachment point $B$ of the cable if the cable length $L_0$ at rest and the force applied at this point are known. It takes into account both the elasticity and deformation of the cable due to its own mass. A drawback of this model is that we will be more interested in a closed-form of the $L_0$ for a given pose of $B$ (for the inverse kinematics of CDPR) and in alternate form of the model that will provide constraint on the force components (for the direct kinematics). We have proposed new original formulations of the Irvine model in [13] and have shown that their use drastically improve the solving time for both the inverse and direct kinematics (i.e finding all possible solutions for both problems) that are required for CDPRs control. Still the solving time of the direct kinematics is too large for the real-time direct kinematics and in that case only the current pose of the platform is of interest.

The direct kinematics relies on an accurate estimation of the cable lengths that is usually based on the measurement of the winch drum rotation. We have evaluated the influence of uncertainties in the cable length measurement on the result of the FK  [19] and have shown that for a poor robot geometry (which was for example the case for the prototype described in section 6.1.2 for which the geometry was imposed) this influence may be quite large . An usual strategy to decrease this uncertainty for small to medium-sized CDPR is to use a drum with a cable spiral guide for the coiling which impose a coiling path for the cable. However this strategy is unfeasible for large and very large CDPR (that we called Ultrabot) for which the large length of the cables impose to have several layers on the drum and therefore leads to a more erratic coiling process that leads to possibly large errors of the cable lengths estimation. To get a better estimation of the cable lengths we have proposed an original method, based on the Vernier principle [21]. The idea is to have several small colored marks on the cable at known distances from the end-point of the cable and to have several color sensors in the mast of the CDPR. We have first shown that if 3 colors (e.g. RGB) were used, then an appropriate disposition of the marks on the cable allows to have up to 29 marks on the cable so that the sequence of 3 successive colors is always unique. Hence by coiling the cable and detecting the 3 successive color detected by a sensor allows to determine exactly the distance between the sensor and the cable end-point, i.e. to calibrate the cable length. Calibration is always an issue for CDPR which uses usually incremental encoders for measuring the drum rotation (which explain why we have also proposed another approach [18]. Then we have considered the sequence of color detection when coiling the cable, starting from its largest length. We have looked at the distribution of cable length changes $\Delta \rho$ between two successive detection and have proposed a strategy that provide the distance between the marks so that this distribution is quasi-uniform with a mean value that is minimal. For example we have shown that for a 60 meters length cable having 29 marks we were able to have an almost constant $\Delta \rho$ of 40 cm, meaning that when the cable length changes by this value, then we get an exact evaluation of the cable length at each detection. In between such detection we rely on the drum rotation measurement to estimate the cable length. Furthermore we have shown that the difference between the expected detection time and the real one allows one to update the estimate of the drum radius, thus enabling to manage an erratic coiling process. We have initially installed this system on the prototype presented in section 6.1.2. The few initial tests were really promising but on-site we have had problems for ensuring a constant positioning of the marks on the synthetic cables. Being given the very short deployment time we have not been able to fix this problem. Consequently we have decided to use another approach based on direct measurement of the load pose with lidars, this approach being described in section 6.1.2.

We have also continued to investigate the calculation of planar cross-sections of the workspace for CDPR with sagging cables. We have shown in a previous paper that the border of this workspace was either determined by cable length limits but also by the singularity of the kinematics equations. Hence these singularities play an important role for the design of a CDPR. We have started a preliminary investigation on this topic  [20]. We have shown that these singularities may be classified in two categories:

• classical singularity which corresponds to the singularity of parallel robots with rigid legs which basically implies that the mechanical equilibrium of the system cannot be obtained, leading to a motion of the platform even if the actuators are locked

• full singularity which are singularity of the kinematics equations but are not classical singularity. In this case mechanical equilibrium is obtained but the CDPR is unable to move in a given direction

We have also developed an algorithm that check if a full singularity exists in the neighborhood of a given pose and to locate it with an arbitrary accuracy.

Cable-Driven Parallel Robots for large scale additive manufacturing

Participants : Jean-Pierre Merlet, Yves Papegay [correspondant] .

Easy to deploy and to reconfigure, dynamically efficient in large workspaces even with payloads, cable-driven parallel robots are very attractive for solving displacement and positioning problems in architectural building at large scale seems to be a good alternative to crane and industrial manipulators in the area of additive manufacturing. We have co-founded in 2015 years ago the XtreeE (www.xtreee.eu) start-up company that is currently one of the leading international actors in large-scale 3D concrete printing.

We have been contacted in 2018 by the artist Anne-Valérie Gasc that is interested in mimicking the 3D additive manufacturing process on large scale for a live art performance. She was interested in a mean for widespreading glass micro-beads on a given trajectory over a 21 $\times$ 9m large platform located at the contemporary art center Les Tanneries (figure 1), located close to Montargis. She was especially interested in using a CDPR for that purpose because of the low visual intrusivity of the cables and its ability to move large load. After a few month of discussions we agree to recycle our old MARIONET-CRANE prototype (2009) for this exhibition although the place was not the most appropriate for the CDPR as the height of the location was only 3 meters. We design as load a 80 liters drum of weight 55 kg with 40 kg of powder that was sufficient for printing one trajectory (figure 1). An on-board computer connected through wifi to a master computer was managing the lidar measurement and the opening/closing of the servo-valve controlling the powder flow. The drum was supported by 4 Dyneema cables of diameter 3mm whose output points were located at the corners of the platform and whose lengths were varying between 3 and 26 meters. The master computer was controlling the CDPR and the parameters of the system were recorded every second in log files. The development was very fast and we were not able to test a full scale installation in our laboratory for lack of the appropriate space. The on-site deployment was difficult because it has to be done in a record time, far away from our home base. The lack of height has especially a strong influence on the positioning errors of the drum that drastically increase if the cables are close to the horizontal. We solve on-site this problem by adding 3 low-cost lidars that were providing partial measurement on the drum pose. The system was fully operational a few days after the official opening of the exhibition and was at the heart of the artistic exhibition "Les Larmes du Prince - Vitrifications" (http://www.lestanneries.fr/exposition/larmes-prince-vitrifications), that was run during July and August under the control of a local student. The exhibition was scheduled to run 5 days per week until the end of August. During this period the CDPR has worked 174 hours (4h15mn/day), has traveled 4757 meters and has dispersed about 1.5 tons of powder. We get two failures: one of the cables has broken but without any consequence because of the redundancy of the robot and a failure of the reduction gear of one of the winch on the exhibition closing day, which has been immediately repaired. From a scientific viewpoint we have been able to test, in this quasi-industrial context, the efficiency of a control law using external measurements of the pose and the logs, still being processed has allowed us to identify possible improvements and scientific issues regarding the modeling of the system. An unexpected benefit of using the lidars was to allow to record a profile of the powder wall at each trajectory, showing its life over time as it was always evolving because of the powder particle motion after a printing.

Killing robots

Participant : Jean-Pierre Merlet [correspondant] .

The director, Linda Blanchet, of a theater company has contacted us for helping organizing a theater event, Killing Robots, centered on the story of Hitchbot, a passive 70cm high mannequin designed by Canadian colleagues, that was put on the side-way of roads in Canada so that people may transport it, the purpose being to study the human interaction with people during a travel from the east to the west cost of Canada. The mannequin was located through a GPS and has taken a picture of its surrounding every 20 minutes while it was active. This mannequin indeed performs this travel in 15 days and a similar experiment was then scheduled in the US, the purpose being to go from Boston to San Francisco. Unfortunately after 5 days of travel the mannequin was discovered completely dismantled in Philadelphia. The idea of Linda Blanchet's performance was to propose a thriller based on the robot data for discovering who has dismantled the robot and in parallel to have the robot interacts with the actors to describe its feeling. For that purpose it was necessary that the robot becomes actuated while keeping its appearance identical to the original model. We have therefore retrieved a clone of the original Hitchbot and we have actuated the arms and head, so that the robot was able to move them, adding a lidar on top of the head so that it was able to locate the actors on stage (figure 2).

The Canadian colleague have also provided a conversational agent so that the robot was able to speak with a learning process. The opening of the performance was done on November 6 at the National theater of Nice and it is now performing in various places in France. We have been present at several of them to interact with the public at the end of the performance. From a scientific viewpoint our interest in this exhibition was to better understand why adding motion to a mannequin modify drastically the perception of the robot by the public. These understanding will help to work on the factors that increase the acceptance of a technological object by the public, which is clearly a major factor for the efficiency of our assistance devices.