## 6 Conclusions  
This paper presents a novel kinematic-model-free control for controlling the pose of multiple points along the kinematic chain of a continuum robot. The proposed controller is able to resolve redundancies and converge faster to a desired configuration. The controller works by actuating the robot using randomly-generated actuation primitives and observing their effects on the control points. This information is then used to build a local linear model using locally weighted dual quaternions. The local linear model is then used to calculate an actuation primitive and actuate the continuum robot towards a desired pose.  
In the first experiment, it was evident that the performance of the controller worsened in terms of convergence when increasing the degrees of freedom of the robot. The higher the degrees of freedom, the longer it took to converge. This is due to the nonlinearities introduced, making the local linear model less accurate.  
We presented the generalized kinematic-model-free multi-point controller and the method by which observations are used to calculate actuation primitives that will reduce the distance between a robot's current pose and its desired target pose. The simulation results in the second experiment show that this novel controller is capable of performing reaching tasks without any prior kinematic model of the robot, successfully actuating the poses of the control points towards some desired configuration.  
Three arrangements for the control points were tested on a simulated 9-degrees-of-freedom continuum robot. Three different robot configurations were targeted, all of which are within the robot's configuration space. It was noted that, when more control points were used, the controller performed better and converged faster to the desired target robot pose. Controlling multiple points along a robot did not only resolves redundancies, but proved to converge faster to the desired pose.  
Finally, the controller's robustness was tested by executing the simulation 100 times using random target configurations which the controller had to reach. The random target  
Figure 8: In this simulation run, the controller attempted to actuate the robot to a back arching configuration. It achieved to reach this configuration within 150 steps.  
configurations lied within the robot's configuration space. The kinematic-model-free multi-point controller succeeded in reaching the target poses within 150 steps 82% of the times.  
The proposed controller can be used in applications where simultaneous translational and rotational reaching of redundant robots is required. The controller is useful for resolving redundancies of continuum robots. The kinematic-model-free approach in general can be used for new robots where a model is not readily-available or for robots that are hard to model. In general, the controller is applicable where flexibility is favored over precision and speed. Examples of such applications include use of soft robots for reaching, drawing, picking-and-placing, etc. As for future work, continuous control, gravity compensation, joint limits, joint friction, and physical implementations, are promising research directions to be investigated. These challenges must be addressed before deploying the kinematic-model-free controller on any physical system.  
[PERSON] developed the theory, methodology, and software, performed the simulation experiments, and wrote the paper. [PERSON] prepared the robot simulation model and interface and reviewed the paper. [PERSON] supervised the research and proofread the paper. All authors have read and agreed to the published version of the manuscript.  
This work was supported through the resources at the Dubai Future Labs. Full financial support for [PERSON]'s PhD program was provided by the UAE's Ministry of Education.  
Not applicable.  
The authors declare no conflict of interest.