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Cable driven parallel robots (CDPRs) are often challenging to model and to dynamically control due to the inherent flexibility and elasticity of the cables. The additional inclusion of online geometric reconfigurability to a CDPR results in a complex underdetermined system with highly non-linear dynamics. The necessary (numerical) redundancy resolution requires multiple layers of optimization rendering its application computationally prohibitive for real-time control. Here, deep reinforcement learning approaches can offer a model-free framework to overcome these challenges and can provide a real-time capable dynamic control. This study discusses three settings for a model-free DRL implementation in dynamic trajectory tracking: (i) for a standard non-redundant CDPR with a fixed workspace; (ii) in an end-to-end setting with redundancy resolution on a reconfigurable CDPR; and (iii) in a decoupled approach resolving kinematic and actuation redundancies individually. 

The addition of geometric reconfigurability in a cable driven parallel robot (CDPR) introduces kinematic redundancies which can be exploited for manipulating structural and mechanical properties of the robot through redundancy resolution. In the event of a cable failure, a reconfigurable CDPR (rCDPR) can also realign its geometric arrangement to overcome the effects of cable failure and recover the original expected trajectory and complete the trajectory tracking task. In this paper we discuss a fault tolerant control (FTC) framework that relies on an Interactive Multiple Model (IMM) adaptive estimation filter for simultaneous fault detection and diagnosis (FDD) and task recovery. The redundancy resolution scheme for the kinematically redundant CDPR takes into account singularity avoidance, manipulability and wrench quality maximization during trajectory tracking. We further introduce a trajectory tracking methodology that enables the automatic task recovery algorithm to consistently return to the point of failure. This is particularly useful for applications where the planned trajectory is of greater importance than the goal positions, such as painting, welding or 3D printing applications. The proposed control framework is validated in simulation on a planar rCDPR with elastic cables and parameter uncertainties to introduce modeled and unmodeled dynamics in the system as it tracks a complete trajectory despite the occurrence of multiple cable failures. As cables fail one by one, the robot topology changes from an over-constrained to a fully constrained and then an under-constrained CDPR. The framework is applied with a constant-velocity kinematic feedforward controller which has the advantage of generating steady-state inputs despite dynamic oscillations during cable failures, as well as a Linear Quadratic Regulator (LQR) feedback controller to locally dampen these oscillations. 

Mobile Cable-Driven Parallel Manipulators (m-CDPM) are a sub-class of CDPM with greater-capabilities (antagonistic cable-tensioning and reconfigurability) by virtue of mobility of the base-winches. In past work, we had also explored creation of adjustable spring-stiffness modules, in-line with cables, which decouple cable-stiffness and cable-tensions. All these internal-freedoms allow an m-CDPM to track desired trajectories while equilibrating end-effector wrenches and improving lateral disturbance-rejection. However, parameter and configuration selection is key to unlocking these benefits.

To this end, we consider an approach to partition task-execution into a primary (fast) winch-tension control and secondary (slow) reconfiguration and joint-stiffness modulation. This would enable a primary trajectory-tracking task together with secondary task-space stiffness tailoring, using system-reconfiguration and joint-stiffness modulation. In this paper, we limit our scope to feasibility-evaluation to achieve the stiffness modulation as a secondary goal within an offline design-optimization setting (but with an eye towards real-time implementation).

These aspects are illustrated in the context of a 3-PRP m-CDPM for tracking a desired trajectory within its wrench-feasible workspace. The secondary-task is the directional-alignment and shaping of the stiffness ellipsoid to shape the disturbance-rejection characteristics along the trajectory. The optimization is solved through constrained minimization of a multi-objective weighted cost function subject to non-linear workspace feasibility, and inequality stiffness and tension constraints.