Research On Stiffness Of A Modular Cable-driven Bio-inspired Robotic Arm

In this dissertation,a modular cable-driven bio-inspired robotic arm(MCBRA)is proposed,inspired by the human arm.The MCBRA consists of a 3-DOF shoulder joint,a 1-DOF elbow joint and a 3-DOF wrist joint in series.Each joint module of the MCBRA is a kind of cable-driven parallel mechanism,where the moving-platform and the base are connected by a passive joint,and the driving cables are employed to replace the rigid components to transfer force.The cable driving units of the robotic arm are all mounted on the base plate.Therefore,the MCBRA has the characteristics of light weight,low moving mass,high payload-to-weight ratio,large workspace,variable stiffness and high security,which is suitable for the application of human-robot cooperation.The MCBRA has a great significance in research and application.In this dissertation,systematic methods of modeling and analysis are proposed for the design,kinematic,statics,stiffness and cable tension distribution of the MCBRA.The main works and contributions of this dissertation are listed below:(1)Inspired by the human arm,a modular,cable-driven,variable-stiffness robotic arm is designed.Besides,in order to increase the vibration range of the stiffness of the driving cable,a novel variable-stiffness device(VSD)is designed based on torsion springs,which is compact in structure and convenient in installation.The VSDs are fixed at the end of the driving cables in series,which can improve the compliance and safety of the MCBRA.(2)The modeling and analysis of the kinematics,statics and stiffness of the joint modules of the MCBRA are proposed.As the cable-driven joint modules are redundantly driven,there exist infinite cable tensions for a joint module at an equilibrium pose.Thus,the cable-driven joint modules have the characteristic of variable stiffness.We can regulate the stiffness of the joint modules by adjusting the cable tensions.(3)The 3-DOF cable-driven joint module is a low-stiffness system and its trajectory is a curve on SO(3).When the applied load increases,the displacement of the 3-DOF cable-driven module is large.Hence,the conventional stiffness identification has low accuracy for the 3-DOF cable-driven module.In this dissertation,we study the motion and load of the 3-DOF joint module on SO(3),and derive a novel stiffness model on SO(3),with introducing the metric matrix,Levi-Civita connection and covariant derivative into SO(3).Based on the approximation of the novel stiffness model and the least square method,a novel stiffness identification method with high accuracy is proposed.(4)In order to achieve the stiffness control of the joint modules of the MCBRA,a stiffness-oriented cable tension distribution method is proposed for the joint modules.For the 3-DOF joint module,it is difficult to solve the cable tensions from the desired stiffness matrix directly,due to the complex stiffness model of the 3-DOF joint modules.The optimization model of the stiffness matrix is employed to solve this issue.Based on the redundant actuation and the equilibrium equations of the joint module,the optimization model is simplified with reduction of decision variables and elimination of equality constraints.As the objective function of the optimization model is too complex to compute the gradient,the gradient-based optimization methods are not suitable for this optimization model.Then,the conventional Nelder-Mead algorithm is revised to solve the nonlinear optimization model with inequality constraints.Based on the revised Nelder-Mead algorithm,the optimal cable tentions of the 3-DOF joint module are obtained for the desired stiffness matrix.(5)Based on the stiffness modeling of the joint modules,the relationship of the end stiffness of the MCBRA and the stiffness of the joint modules is proposed.Meanwhile,in order to achieve the stiffness control of the MCBRA,a stiffness distribution method is proposed for the MCBRA.As the stiffness model of the MCBRA is complicated,an optimization model of the stiffness matrix is employed to solve this issue of stiffness distribution.Utilizing the redundant actuation and equilibrium equations of the MCBRA,the optimization model is simplified with reduction of decision variables and elimination of equality constraints.The revised Nelder-Mead algorithm is employed to solve the nonlinear optimization model and obtain the stiffness of each joint module.In summary,a systematic research on the design,modeling and analysis of the MCBRA is implemented in this dissertation.Some key issues of the stiffness of the MCBRA have been solved,such as stiffness modeling of the joint modules,stiffness identification of the 3-DOF joint module,cable tension distribution of the joint modules,stiffness modeling and stiffness distribution of the MCBRA.These results build up a basis for the research and application of the MCBRA.