Prototype design and time-optimal control of a lower-mobility cable-driven parallel robot

Abstract

Cable-driven parallel robots (CDPRs) combine the properties of parallel robots with the characteristics of flexible cables, which bring them plenty of potential merits. However, the flexibility and unilateral property of cables causes difficulties in the design, planning and control of CDPRs and hinder the expansion of their applications. To mitigate these difficulties, this thesis investigates a systematic methodology for the development of a novel lower-mobility CDPR and addresses the time-optimal path following problem of the proposed robot. Firstly, this thesis presents a novel suspended CDPR with an articulated reconfigurable moving platform to generate Schönflies motions and enhance the rotational capability. The proposed robot uses four pairs of parallel cables to constrain the redundant motions. The moving platform consists of one end-effector and two subplatforms which are articulated through revolute joints. A gearbox is embedded in the moving platform to amplify the rotational motion about the vertical axis. For the proposed robot, the kinematic and dynamic modeling is given in detail. The multi-objective optimal design is conducted to determine the dimensional parameters. The reconfiguration of the moving platform is formulated as an optimization problem and demonstrated through a case study. The interference-free static workspace is determined through a numerical approach. A prototype of the proposed robot is fabricated, and experimental tests are performed to evaluate the feasibility of the proposed robot. Secondly, this thesis proposes a novel method for time-optimal time scaling (TOTS) subject to third-order constraints. The proposed method formulates the third-order TOTS as a four-stage optimization involving only linear pro­gramming by exploiting the special structure of the problem. The proposed method first performs a backward pass and a forward pass to generate the second-order optimal velocity profile. Then the points violating the third­-order constraints are identified, and the constraint violations are eliminated through numerical integration around the violating points. A bisection search algorithm is proposed to quickly determine the switching points at which the elimination process begins. The proposed method is verified through numerical examples and experimental tests. The results indicate that the proposed method outperforms the state-of-the-art approaches in terms of solution quality and computation time. Thirdly, this thesis proposes a look-ahead online scaling approach to generate feasible trajectories of CDPRs subject to cable velocity, acceleration, jerk and tension constraints. The proposed approach follows the path-velocity decomposition scheme. Based on the desired path, the constraint equations are converted into the equivalent bounds on the path states by a look-ahead bounds estimation module. Then the timing law is online scaled by three cascaded controllers to fulfill the estimated bounds. The scaled timing law and the desired path are combined to form the final trajectory. Comparative studies on the CDPR prototype demonstrate that the proposed approach outperforms state-of-the-art methods in terms of solution quality and compu­tation time. Finally, this thesis presents a real-time model predictive control (MPC) scheme for jerk-limited time-optimal path following control of CDPRs. The proposed MPC scheme solves the control inputs and the timing law of the desired path by simultaneously minimizing the path following error and maximiz­ing the path progress subject to the input and state constraints. To reduce computational complexity, a convex MPC formulation is derived by itera­tively linearizing the dynamics and constraints. A high-speed solver for the proposed MPC is developed by leveraging the iterative linear quadratic reg­ulator (iLQR) algorithm and the augmented Lagrangian (AL) method. The feasibility and robustness of the proposed method are validated on the CDPR prototype through simulations and experiments. The results demonstrate that the proposed method outperforms the state-of-the-art method in terms of motion accuracy and motion smoothness.