Motion Planning for Continuum Robots: A Learning from Demonstration Approach

This paper proposes a method to deform a continuum robot into a complex shape with distributed curvature using a single motor drive. This continuum robot can be deformed to a desired shape by placing tendon guides at appropriate intervals. We used several target shapes, including clothoid and sin curves, as well as a circular curve of constant curvature and confirmed that the deformed shapes match them both in the simulation and prototype. This paper proposes two models of continuum robots. One is the Plain Model in which the tendons are parallel to the rod and the Penetration Model in which the tendon penetrates to the rod. By placing the penetrating position(s), this continuum robot can be deformed into a shape with inflection point(s). We designed a mathematical model to simulate the deformed shape of the prototype to obtain the proper placement of the guides and penetration point(s). Through the optimization, it was able to find the parameters that, in most cases, result in the error of less than 4% between the target and deformed shapes on simulation. We applied these conditions to the prototype and evaluated the errors, which were approximately 10%, the same as the related works that use a conventional constant curvature model. We think that the results of this paper can be applied to reduce the number of actuators required and the size and weight of continuum or biomimetic robots.

Kinematic modeling is essential for planning and controlling continuum robot motion. The traditional Denavit Hartenberg (DH) model involves complex matrix multiplication operations, resulting in computationally intensive inverse solutions and trajectory planning. Solving position and orientation changes in continuum robots using the double quaternion rule can reduce computational complexity. However, existing dual quaternion methods are direct equational transformations of DH rules and do not give a complete modeling process. They usually require more interpretability when applying continuum robot kinematic modeling. This paper uses the dual quaternion method to establish a kinematic model of a continuum robot. It uses a two-section continuum robot model to compare the advantages of dual quaternion and traditional modeling methods. In addition, this paper proposes a five-polynomial interpolation algorithm based on the dual quaternion method for trajectory planning of continuum robots. This method accurately models spatial bending and torsional motions of singularity-free continuum robots.

Kinematics optimization and static analysis of a modular continuum robot used for minimally invasive surgery.

As robots begin to move from structured industrial environments to the real world, they must be equipped to not only safely interact with the environment, but also reason about how to leverage contact to perform tasks. In this work, we develop a modeling and motion planning framework for continuum robots that accounts for contact anywhere along the robot. We first present an analytical model for continuum manipulators under contact and discuss the ideal choice of generalized coordinates given properties of the manipulator and task specifications. We then demonstrate the utility of our model by developing a motion planning framework that can solve a diverse set of tasks. We apply our framework to end effector path planning for a soft arm in an obstacle-rich environment, and grasp planning for soft robotic grippers, where contact can happen anywhere on the arm or gripper. Finally, we verify the utility of our model and planning framework by planning a grasp with a desired contact force for a soft antipodal gripper and testing this grasp in a hardware demonstration. Overall, our model and planning approach further enhance soft and continuum robots where they already excel: utilizing contact with the world to achieve their goals with a gentle touch.

Learning from Demonstration (LfD) is a family of methods used to teach robots specific tasks. It is used to assist them with the increasing difficulty of performing manipulation tasks in a scalable manner. The state-of-the-art in collaborative robots allows for simple LfD approaches that can handle limited parameter changes of a task. These methods however typically approach the problem from a control perspective and therefore are tied to specific robot platforms. In contrast, this paper proposes a novel motion planning approach that combines the benefits of LfD approaches with generic motion planning that can provide robustness to the planning process as well as scaling task learning both in number of tasks and number of robot platforms. Specifically, it introduces Dynamical Movement Primitives (DMPs) based LfD as initial trajectories for the Stochastic Optimization for Motion Planning (STOMP) framework. This allows for successful task execution even when the task parameters and the environment change. Moreover, the proposed approach allows for skill transfer between robots. In this case a task is demonstrated to one robot via kinesthetic teaching and can be successfully executed by a different robot. The proposed approach, coined Guided Stochastic Optimization for Motion Planning (GSTOMP) is evaluated extensively using two different manipulator systems in simulation and in real conditions. Results show that GSTOMP improves task success compared to simple LfD approaches employed by the state-of-the-art collaborative robots. Moreover, it is shown that transferring skills is feasible and with good performance. Finally, the proposed approach is compared against a plethora of state-of-the-art motion planners. The results show that the motion planning performance is comparable or better than the state-of-the-art.

Continuum robots are promising for minimally invasive surgery. They consist of thin and flexible structures whose shape can be continuously deformed using re- mote actuators, allowing them to be inserted in small tubular cavities. For safety reasons, it is important to be aware of the forces applied to surrounding tissue during deployment. Because common force sensors are too cumbersome to be embedded into continuum robots, alternative shape-based force estimation methods have been developed. Such methods estimate the contact location and the corresponding force based on the com- parison between a measured robot shape (for instance using Fiber Braggs Gratings sensors or vision sensors) and the one predicted from robot modeling (typically computed using Cosserat rod modeling and actuator po- sitions [1]). The applied force is then estimated through optimization procedures, with [2] or without [3], [4] explicit knowledge of the force application point. These algorithms have shown promising performance but are restricted to passive Cosserat rods models, whereas in practice continuum robots are active structures. Recently, Aloi et al. extended the work from [4] in the case of a 2- DOF tendon-driven robot, for which they experimentally validated their method [5]. All the previous solutions have two limitations. First, they assume contact forces to be perpendicular to the robot’s curvilinear axis: hypothesis (H1). Since con- tinuum robot shapes can be highly curved, one might question how strongly the tangential component of the force can affect the global deformation of the robot. Second, they consist of iterative optimizations during which the whole robot model is computed at each iteration using convex optimization routines. Such an approach can be computationally time-consuming and does not necessarily yield a global optimum. The present paper introduces a new Compliance-based approach to estimate an external force applied to a continuum robot in any direction. Results obtained with a simulated Concentric Tubes Continuum Robot (CTCR) are presented and discussed.

The design and analysis of continuum robots have consistently been a prominent research focus in the field of mechanics. However, portable continuum robots with minimal spatial occupancy, which have great potential for applications such as search and rescue, are scarcely available. This paper presents a novel helical-coiled multi-segment flexible continuum robot featuring helical deployment and compact design, with an integrated framework for structural design, kinematic modeling, and experimental validation. The design of the helical-coiled multi-segment flexible continuum robot for unstructured environment detection, including a flexible body, an actuation module, a feed module, and a sensing module, is presented systematically. Kinematic models of both single- and multi-segment continuum robots were established based on the constant curvature model to analyze the parameter mapping relationship from the end-effector position and orientation to the driving inputs. Furthermore, the feedforward motion of the robot was examined, and an uncoiling strategy based on S-curve compensation was employed to complete the kinematic analysis. Finally, the accuracy of the kinematic model considering the active uncoiling feed motion was validated through experimental analysis, demonstrating the motion characteristics of the continuum robot. Altogether, this study provides a framework for the design and analysis of helical-coiled continuum robots.

In this paper, neural networks are presented to solve the inverse kinematic models of continuum robots. Firstly, the forward kinematic models are calculated for variable curvature continuum robots. Then, the forward kinematic models are implemented in the neural networks which present the position of the continuum robot’s end effector. After that, the inverse kinematic models are solved through neural networks without setting up any constraints. In the same context, to validate the utility of the developed neural networks, various types of trajectories are proposed to be followed by continuum robots. It is found that the developed neural networks are powerful tool to deal with the high complexity of the non-linear equations, in particular when it comes to solving the inverse kinematics model of variable curvature continuum robots. To have a closer look at the efficiency of the developed neural network models during the follow up of the proposed trajectories, 3D simulation examples through Matlab have been carried out with different configurations. It is noteworthy to say that the developed models are a needed tool for real time application since it does not depend on the complexity of the continuum robots' inverse kinematic models.

Continuum Robots The cover illustrates three continuum robots accessing a nuclear facility through pipes, with a pneumatically actuated robot manipulating a radioactive component, a tendon-driven continuum robot performing a laser machining task on it, and a concentric tube robot monitoring the operation. In article number 2200367, recent advances, current limitations, and open challenges in the design, modeling, and control of continuum robots are discussed by Matteo Russo, Dragos Axinte, and colleagues.

Continuum robots have the potential to enable new applications in medicine, inspection, and countless other areas due to their unique shape, compliance, and size. Excellent progress has been made in the mechanical design and dynamic modeling of continuum robots, to the point that there are some canonical designs, although new concepts continue to be explored. In this paper, we turn to the problem of state estimation for continuum robots that can been modeled with the common Cosserat rod model. Sensing for continuum robots might comprise external camera observations, embedded tracking coils, or strain gauges. We repurpose a Gaussian process (GP) regression approach to state estimation, initially developed for continuous-time trajectory estimation in SE(3). In our case, the continuous variable is not time but arclength and we show how to estimate the continuous shape (and strain) of the robot (along with associated uncertainties) given discrete, noisy measurements of both pose and strain along the length. We demonstrate our approach quantitatively through simulations as well as through experiments. Our evaluations show that accurate and continuous estimates of a continuum robot’s shape can be achieved, resulting in average end-effector errors between the estimated and ground truth shape as low as 3.5 mm and 0.016° in simulation or 3.3 mm and 0.035° for unloaded configurations and 6.2 mm and 0.041° for loaded ones during experiments, when using discrete pose measurements.

Continuum robot, unlike conventional rigid-link robots, has numerous numbers of degrees of freedom, enabling it to be applied for confined space works, such as minimally invasive surgery, safe robot/objective interactions, and in-situ aero-engine detection. This study presented a cable-driven continuum robot with twin-pivot structure, which poses smaller diameter-length-ratio and torsion resistance ability compared with conventional single-pivot structure, as well as the kinematics and shape estimation. The kinematics model of the twin-pivot continuum robot is established based on the assumption of piecewise constant curvature, with which the mapping between driving space and operation space are presented. Finally, a prototype of continuum robot system with single section is constructed to verify the validation of the kinematics model and study the shape estimation. Based on the constructed prototype, the shape estimation of the continuum robot with different payloads is performed. The comparative results suggest that relative error is less than 5% for total length of the single section without payload, verifying the validity of the kinematics model. The comparison between the results with different payloads indicate that the increasing payload will increase the relative error.

Whole-body motion and footstep planning for humanoid robots with multi-heuristic search

Continuum robots have the advantages of agility and adaptability. However, existing continuum robots have limitations of low stiffness and complex motion modes, and the existing variable stiffness methods cannot achieve a wide range of stiffness changes and fast switching stiffness simultaneously. A continuum robot structure, switching stiffness method, and motion principle are proposed in this article. The continuum robot is made up of three segments connected in series. Each segment comprises multiple spherical joints connected in series, and the joints can be locked by their respective airbag. A valve controls each airbag, quickly switching the segment between rigidity and flexibility. The motion of the segments is driven by three cables that run through the robot. The segment steers only when it is unlocked. When a segment becomes locked, it acts as a rigid body. As a result, by locking and unlocking each segment in sequence, the cables can alternately drive all the segments. The stiffness variation and movement of the continuum robot were tested. The segment's stiffness varies from 36.89 to 1300.95 N/m and the stiffness switching time is 0.25-0.48 s. The time-sharing control mode of segment stiffness and motion is validated by establishing a specific test platform and a mathematical model. The continuum robot's flexibility is demonstrated by controlling the fast bending of different segments sequentially.

Traditional dynamic models of continuum robots are in general computationally expensive and not suitable for real-time control. Recent approaches using learning-based methods to approximate the dynamic model of continuum robots for control have been promising, although real data hungry—which may cause potential damage to robots and be time consuming—and getting poorer performance when trained with simulation data only. This paper presents a modelbased learning framework for continuum robot closed-loop control that, by combining simulation and real data, shows to require only 100 real data to outperform a real-data-only controller trained using up to 10000 points. The introduced data-efficient framework with three control policies has utilized a Gaussian process regression (GPR) and a recurrent neural network (RNN). Control policy A uses a GPR model and a RNN trained in simulation to optimize control outputs for simulated targets; control policy B retrains the RNN in policy A with data generated from the GPR model to adapt to real robot physics; control policy C utilizes policy A and B to form a hybrid policy. Using a continuum robot with soft spines, we show that our approach provides an efficient framework to bridge the sim-to-real gap in model-based learning for continuum robots.

This paper describes a state estimation model for a multi-segment continuum robot that utilizes the displacement of passive cables embedded along the robot's length to estimate its overall shape. As continuum robots are used in activities outside a laboratory environment, methods of measuring their shape configuration in real-time will be necessary to ensure robust closed-loop control. However, because these robots deform along their entire length and lack discrete joints at which primary displacements take place, conventional approaches to sensing joint displacement (e.g., encoders) are inappropriate. Furthermore, elasticity plays a key role in determining the resulting shape of the continuum robot, instead of the mechanics-independent kinematic configuration frequently seen in rigid-link robotics. In order to enable accurate estimates of a continuum robot's shape, the measured displacements of passive cables are utilized to detect the change in shape of the continuum robot. An optimization is used with a static model based on the principle of virtual power to map these cable displacements into the resulting continuum robot configuration. This state estimation model was implemented numerically in MATLAB and validated on an experimental test platform.