Section: New Results

Robotics

Cable-driven parallel robots (CDPR)

Analysis of Cable-driven parallel robots

Participants : Alessandro Berti, Laurent Blanchet, Houssein Lamine, Jean-Pierre Merlet [correspondant] , Yves Papegay, Rémy Ramadour.

We have continued the analysis of suspended CDPRs for control and design purposes. For control it is essential to determine the current pose of the robot for given leg lengths. This forward kinematic problem (FK) is usually very complex and admits several solutions. For parallel robot with rigid legs we have established the important property (P) that the FK may be solved in real-time i.e. being given the leg lengths $\rho$ and platform pose $𝐗$ it is possible to determine the single pose ${𝐗}_{\mathbf{1}}$ that can be reached from $𝐗$ if the leg lengths has been changed to $\rho +\Delta \rho$ provided that $\Delta \rho$ satisfies some properties. For CDPR with sagging cables determining all the FK solutions is more complex but we have proposed the first algorithm to solve it the for a full scale model of sagging cables  [24] . For CDPR with non sagging cables the problem is also very complex because we cannot make any assumption on the number of cables under tension i.e for a CDPR with $m$ cables we have to solve all the FK problems for all possible set of cables under tension from 1 to $m$ and as soon as this number is lower than 6 the system of equations is much larger than for classical robots. We have however been able to propose an interval analysis based algorithm that allow one to get all the solutions  [18] . But we have also shown that for non sagging cables the property (P) does not hold. Indeed it requires that the system of equations that governs the FK remains the same at all time. But for CDPR this system depend on the set of cables under tension (which is called the cable configuration CC) and it may change when the cable lengths change from $`\rho$ to $\rho +\Delta \rho$, even for redundant CDPR  [23] . If the CC changes at some point the pose solution of the FK together with the cable tensions will differ from the one that is obtained when assuming no change in the CC. This has a drastic effect on control as we have now a system whose state equations may change over time but also on design as in the new CC the cable tensions may be quite different from the expected one. Hence property (P) will hold if and only if we are able to show that there will not be any change in the CC during the change of the cable lengths and therefore it is crucial to detect CC changes. But this require to fully simulate the discrete-time control laws together with the behavior of the coiling system. We have been able to implement a simulation tool that tracks a trajectory for the robot for arbitrary control laws and coiling system model  [22] , [25] . The principle of the algorithm is to determine if on a time interval $[t,t+\delta t]$ the solution of the FK with the current CC satisfies (P) by using Kantorovitch theorem. If this is not the case $\Delta t$ is divided by 2 and the process is repeated. We then check if there is a time $t_1$ in $[t,t+\delta t]$ for which the tension of a cable in the CC may become 0 If there is no such $t_1$ for any cable in the current CC, then it will be the CC at time $t+\delta t$ and we may compute the pose and cable tensions at any time in $[t,t+\delta t]$. If there is a least one such $t_1$ (and there may be several $t_1^i,t_1^j,...$ as we consider each cable in the CC) we order these times by increasing values and check sequentially if a cable tension become negative with the current CC at time $(t_1^i+t_1^{i+1})/2$. If yes we determine what can the CC at this time by looking at all possible CC. As soon as the new CC at time $t_1^i$ has been determinated the simulation can go on. Implementing this algorithm has been difficult mainly for numerical reasons: the accuracy of the calculation may sometime exceed the floating point accuracy and we have to resort to symbolic computation and extended arithmetics. Our tests have shown that indeed CC changes may occur on trajectories: on a typical trajectory up to 10 different CC will appear with 5 or 6 cables under tension. These results have been confirmed experimentally on a prototype at LIRMM.

Tool for Agencement Analysis and Synthesis of CDPRs

Participants : Laurent Blanchet, Jean-Pierre Merlet [correspondant] .

HEPHAISTOS has been working on tools to design the layout and geometry of CDPRs, while accounting for numerical errors as well as practical errors – actual position of the winches, of the attachments on the platform, errors of the controllers, of the cables, etc. Within this work, collision analysis plays an important role. Indeed the concept of cable robot aims to increase the workspace that is restricted for robots having rigid legs but interferences may reduce this workspace. Two types of interference analysis approaches exist: intersection of numerically-mapped boundaries (InB) and distance between features (DbF). The two sets of interference types that can be analysed using these approaches are distinct but overlapping. The first approach greatly benefits from Inria's computational geometry research and particularly from the AABB tree algorithms implemented in CGAL. Algorithms and implementation based on those were developed, along with several new algorithm and implementation to extend the scope of intersection types, and thus, of interference types. Algorithms to improve efficiency of given intersection types were also developed. We have already used the second approach, DbF, to develop algorithms for leg interference of parallel robots that are very efficient for non deformable cables but now well adapted for sagging cables. An interference detection algorithm has been developed and implemented for a restricted scope of applications [10] , and research is on-going for a more generic case.

Visual-servoing of a parallel cable-driven robot

Participants : Rémy Ramadour, Jean-Pierre Merlet [correspondant] , François Chaumette [correspondant] .

The last two years, we studied how visual servoing could improve accuracy, controllability and performance of cable-driven parallel robots [13] . Previous works on this domain showed very interesting results but some issues remained to be investigated , such as :

• ratio accuracy/workspace : cable-driven parallel robots are known to allow a large reachable workspace, but also to have complex geometric and dynamic models which affect the accuracy. Using visual-servoing in a closed-loop scheme, we were able to enhance the accuracy by a factor of ten, allowing to manipulate daily-life objects in a whole living room.

• image-based joint-space control : in order to reach a desired pose, the usual method involves several computing and evaluations of both the Jacobian matrix of the manipulator and the interaction matrix linking visual features to the displacements of the end-effector. We designed a control scheme, based on an iterative updating using the Broyden update law, in order to link the visual features directly to the joint coordinates. This scheme is less sensitive to model uncertainties and require much less computing.

• stability of the command law : classical control laws ignore cable configuration effects that change the pose of the platform. We have proposed a counter-intuitive strategy: the robot MARIONET-ASSIST we are using has a specific geometry that allow to predict which cables set may be under tension for a given trajectory i.e. we are able to split the trajectory in parts for which we know all possible cables configurations. Among them we select the one that optimize an accuracy criteria and we enforce it by forcing the cables not part of the configuration to be slack by adding a sufficient amount of length to their nominal values. It allowed to enhance both the stability and the accuracy of a vision-based control scheme  [26] .

We also used interval analysis in order to guaranty every step of the process, in order to provide safety and reliability of our methods, as the robots that we use were initially deployed in the context of assistive technologies.

Finally, simulations and experiments on prototypes were conducted and presented in order to validate the mentioned results. However, the prototype that we used presents a very particular configuration (all wires are connected to the same point on the end-effector, allowing only translational movements), further works may be required in order to test our methods for a wider variety of cable-driven parallel robots.

Cable-Driven Parallel Robots for additive manufacturing in architecture

Participant : Yves Papegay.

Easy to deploy and to reconfigure, dynamically efficient in large workspaces even with payloads, cable-driven parallel robots are very attractive for solving deplacement and positioning problems in architectural building at scale 1 and seems to be a good alternative to crane and industrial manipulators in this area.

In a collaboration with CNAM and Ecole Nationale Supérieure d'Architecture Paris-Malaquais, we aim to design and realize a CDPR of large size as a proof of concept in additive manufacturing of building based on ultra-high performance concrete.

Challenges are modeling and control to get enough accuracy.

Assistance robotics

This is now the core of our activity and our work on CDPR is deeply connected to this field as they are an efficient solution for mobility assistance, a high priority for the elderly, helpers and medical community. We have presented our vision of assistance robotics in several occasions [20] , [21] , [19] .

Assessment of elderly frailty

Participants : Karim Bakal, Jean-Pierre Merlet.

The assessment of elderly frailty is a difficult concept because it involves the physical capacities of a person and its environment (health-care services, families, funds...). We consider the assessment of upper limb capabilities by looking at the joint torques $\tau$ of the arm and the maximal force $F$ that can be exerted by the hand, which are related by the equation

where $𝐉$ is a matrix which depends only upon the configuration of the arm. This equations constitutes an underconstrained linear system. In biomechanics the torque $\tau$ is measured together with the configuration of the arm and the force $F$ is evaluated by using the method of Chiacchio, that involves the pseudo-inverse of ${𝐉}^{𝐓}$ to calculate $F$. But there are several uncertainties that are neglected when using this method: the measurement errors on $\tau$ and on the configuration of the arm together with uncertainties on the physical parameters of the arm (such as the length of the bones). The method of Chiacchio provides one of the possible solutions of equation (2 ) and not necessary the one corresponding to the force at the hand. We use another approach based on interval analysis. We assume that all uncertainties may be bounded ($\tau$ is an interval vector ${\tau }_m$, ${𝐉}^{𝐓}$ is an interval matrix) so that equation (2 ) become an interval linear system. Interval analysis then allows one to determine an approximation as accurate as wanted of the set $F_s$ of all forces $F$ that satisfy the equation and therefore this set includes the real force at the hand. Now assume that with the same arm configuration we measure the force at the hand, here again with some bounded uncertainties (i.e. $F$ is an interval vector $F_m$). Here again we may use interval analysis applied on equation  (2 ) in order to determine an interval vector ${\tau }_v$ for the $\tau$ that is guaranteed to include the real $\tau$. Furthermore $\tau$ must be included in the intersection ${\tau }_i$ of ${\tau }_v$ and ${\tau }_m$ while $F$ must be included in the intersection $F_i$ of $F_m$ and $F_s$. If ${\tau }_i$ is strictly included in ${\tau }_m$, then we may compute a better approximation of $F_s$. Reciprocally if $F_i$ is strictly included in $F_m$ we will get a better ${\tau }_v$. If one of these situation occurs we repeat the process until no significant improvement of $F_s$ or ${\tau }_v$ is obtained. In a second step we consider that the uncertainties that lead to uncertainties in the matrix ${𝐉}^{𝐓}$ are constrained as we have to satisfy ${\tau }_v={𝐉}^{𝐓}{F}_s$. Here again we use interval analysis to determine if this constraint does not allow to reduce the size of the interval on the physical parameters in which case we may obtain a new ${𝐉}^{𝐓}$ that is included in the initial one. In turn this may allow to obtain better ${\tau }_v$ and $F_s$. The process stops when no improvement has been obtained for $F_s$, ${\tau }_v$ and the physical parameters.

To test this approach the right upper limb joint torque of 10 males and the force capacity at the right hand was measured by a dynamometer (Biodex III, Biodex Medical Systems) and respectively by a 6-axis load sensor during an experiment performed at HandiBio laboratory. The configuration of the upper limb was measured with a motion capture system (Qualisys, Sweden). The approach is currently being evaluated.

Walking analysis

Participants : Claire Maillard, Ting Wang, Jean-Pierre Merlet [correspondant] .

The walkers of the ANG family allow one to determine accurately the trajectory of the walker and therefore to analyse the walking of the user. We have used this property for performing until mid 2013 a large scale experiment: 23 young adults and 25 elderly people ($>$ 69 years) were asked to walk along with two reference trajectories with the help of the walker. The objective of this research is to develop walking quality index and examine if the walker may be used to monitor the health state of elderly people at home. We compared and statistically analyzed the walking patterns of the two groups of people. The results show that it is possible to obtain new indicators by using the walker measurements [9] ,[14] . Next step will be to perform a similar analysis for a sit-to-stand (STS) exercice and to test our approach in two rehabilitation centers, MATIA in Spain (in the framework of the RAPP project) and Centre Héliomarin de Vallauris.

A start-up plan was proposed in November 2014 to transfer the walking analysis technology of Hephaistos with the ANG walker. In order to study the feasibility of our plan, we have interviewed Patrick Nenert (Kiné, Centre Hélio-Marin), Françoise Dubourgeois (DR, EPHAD) and Sophie Morgenstern (Métropole NCA, Living Lab Paillon 2020) about their impression of the walker and the possibility of the future collaboration with them. Several contact with local actors of the silver economy sector have already been established : Livinglab Paillon2020 (Nice), CIU-santé, as well as with research lab for collaboration on future projects (Lapcos, I3M, Gredeg).

Design and evaluation of assistive devices, ethics

Participants : Marc Beninati, Bernard Senach [correspondant] , Jean-Pierre Merlet.

Providing appropriate support, services and information to the elderly, to their caregivers and to the medical profession, through a fleet of communicating devices must rely on a structured processes. A generic design and evaluation framework is being elaborated and will be validated through field experiments.

Assistance robotics raises many ethical questions. We started reflection about conducting experiments with frail and old people. A listing of questions to be addressed at each step of an experiment has been written (internal document). We have also hired a joint PhD student with University Bologna about the legal aspects of assistance robotics and we plan to organize a national forum on this topic with Nathalie Nevejans from University of Douai.