Optimal Path Planning and Reconfiguration Strategy for Reconfigurable Cable Driven Parallel Robots

Cable-Driven Parallel Robots (CDPRs) are a class of parallel robots whose legs are composed of cables. The cables are fixed to a mobile platform and the robot base frame. CDPRs are limited by the cable interferences and the collisions between cables and environment. Reconfigurable Cable-Driven Parallel Robots (RCDPRs) are able to reduce these drawbacks. By reconfigurable, we means that the cable exit points can be displaced into different locations. Our research works aim at: computing the optimal reconfiguration strategy, in order to reduce the number of reconfigurations; computing the optimal path planning, by selecting the order of the via points which minimizes the path length. The optimization is performed by means of a graph optimization, modelling the problem as a Chinese Postman Problem. During the last decades, parallel robots have been widely developed. They are composed of a platform connected to a base frame by several legs. Usually, each leg consists of a kinematic chain of rigid links and joints. In the 90’s researchers developed a new class of parallel robots, the Cable Driven Parallel Robots (CDPRs), substituting the rigid legs with cables. An image of a CDPR is illustrated in Fig. 1. The cable connection points with the platform are defined hereafter as cable anchor points. The other end of the cable is rolled on a motorized winch. The cables are connected to the robot base frame through passive pulleys. Pulleys guide and orient the cables with respect to the position assumed by the platform. The contact point between the cables and the pulleys are defined hereafter as cable exit points. The main advantages of CDPRs are their large workspace and an high payload to weight ratio. On the contrary, the non-rigid nature of the cables reduces the platform positioning precision and demands a careful analysis of CDPR stability conditions, considering that cables can only pull but not push the platform. According to the previous advantages and drawbacks, CDPRs have been used in several industrial applications, e.g. the displacement of heavy payloads (Nguyen et al. 2014), the painting of air-planes (Albus, Bostelman, and Dagalakis 1992) or as support platform for wind tunnel (Sturm, Wildan, and Bruckmann 2011). Figure 1: Example of RCDPR developed in the framework of CAROCA Project. In order to investigate and improve the use of CDPRs in an industrial context, the IRT Jules Verne, a french research institute, promoted the CAROCA Project (Evaluation des CApacités de la RObotique CÂbles dans un contexte industriel). CAROCA Project mainly focuses on the analysis and development of Reconfigurable Cable Driven Parallel Robots (RCDPRs). RCDPRs distinguish themselves for the possibility of modify their geometric parameters, and in particular the position of their exit points. In our specific case, pulleys can be moved among a set of discrete position defined by the designer of the robot (as illustrated in Fig. 1), avoiding cable interferences, collisions with the environment, and adapting the CDPR performances according to the demanded applications. RCDPRs have been already investigated by several research teams. Most of the research work performed on the subject is related to the design, modelling and control of RCDPRs. Our research work focused as well on the design of CDPRs and RCDPRs, as in (Gagliardini et al. 2014) or in (Gagliardini et al. 2015b). More in particular, we proposed a design strategy for RCDPR to be used in an industrial domain. The designed RCDPRs can move their exit points along a predefined grid of locations. For this kind of RCDPRs, no particular analysis has been performed in terms of platform path planning and exit point reconfiguration strategy. Based on our previous research work, we proposed in (Gagliardini et al. 2015a) a novel method to compute Figure 2: Example of a feasibility chart and the associated graph graph developed for configurations C1 and C2. Np,j,k represent the nodes generated at point Pp of the prescribed path, contemplating a reconfiguration from Cj to Ck. the reconfiguration strategy for the exit points of the RCDPR. Generally, several configurations can be used in order to complete a task. The proposed algorithm aims at defining the optimal order of reconfigurations to be used. Several criteria can be optimized, e.g. the number of reconfigurations, and the capacity margin of the robot (Guay et al. 2013). The desired path of the platform is given by the user. The optimization takes into account a set of constraints, including: the platform static and the dynamic equilibrium, the cable interferences and the cable collisions with the environment, the platform positioning precision. The analysis of the constraints let compute a feasibility chart of the poses composing the desired path/ A pose is feasible if a list of constraints is satisfied. An example of chart is illustrated in Fig. 2. The optimization is performed by means of a graph approach. The nodes of the graph represent the possible reconfigurations and the poses of the prescribed path when the reconfigurations occur. Reconfigurations are taken into account in two cases: when a configuration Ci becomes infeasible at point Pp of the prescribed path and we can move to a feasible configuration Cj ; when a configuration Ci becomes feasible at point Pp of the prescribed path and we can move to it from another feasible configuration Cj . Fig. 2 illustrates an example of graph. The limit of the proposed strategy is associated to an absence of a path planning. Some task may demand to cover a wide workspace, e.g. the painting of the tubular structure illustrated in Fig. 3: during the painting the platform follows all the red segments of the path defined by the user. The order of passage through the different segments influences the performances of the CDPR and the length of the desired path (which increases when the platform as to pass two times along the same segment). The optimal path planning can be computed defining the optimal Hamiltonian cycle approaching the problem as a Chinese Postman Problem (CPP) (Roberts and Tesman 2009). The novel approach suggests to optimize both the reconfiguration strategy and the path planning. The Figure 3: Example of structure to be painted. The prescribed path is illustrated by a set of red segments. Figure 4: planar example of a task demanding to follow 5 red segments. The blue arc has been used create an Hamiltonian graph. The cost of each arc is computed analysing the reconfigurability strategy associated to each path, as illustrated for the lower segment. developed strategy performs a graph optimization based on a mix method: (i) the selection of the optimal path is performed analysing the problem as a CPP. Given a set of segments to be covered, a graph is created generating a node for each segment to cover and connecting the nodes by arcs when two segments are adjacent. (ii) The cost of each arc is computed analysing the feasibility map of each segment, transposing it into a graph and solving it by means of a Dijkstra’s algorithm. A summary of the procedure is illustrated in Fig. 4. In conclusion, the proposed method aims at solving both the length of the path to be followed and the reconfiguration strategy. Despite the low computational time demanded to solve the graph, the main drawback is associated to the computational time demanded to build the feasibility chart necessary to the graph creation.