Continuum robots inspired by biological life forms are favored for their flexibility, compliance, and adaptability to confined environments. However, flexible structure and coupled dynamics include challenges, especially under external forces. This paper presents a dynamic-model-based control framework for a two-section planar-to-spatial tendon-driven continuum manipulator (P2S-TDCM), which integrates a comprehensive Euler–Lagrange model that accounts for tendon stiffness, viscous damping, and backbone flexibility. A genetic algorithm (GA)-optimized PID controller is designed and tested on deterministic and robustness-oriented tuning modes. To further enhance real-time robustness against external disturbances, an online disturbance observer (DOB) is integrated into the control loop to estimate and compensate for unmeasured external wrenches. Numerical results showed that the robust tuning strategy achieved consistently lower RMSE (up to ∼ 25% improvement compared to the deterministic approach) and reduced sensitivity to parameter uncertainties such as vertebra mass by ±2%, backbone Young’s modulus by ±5% under external tip forces. Experimental validation of the deterministic controller further confirmed the model’s accuracy and feasibility. The combined GA-PID-DOB framework improves trajectory tracking stability and disturbance rejection, establishing a robustness-oriented control for P2S-TDCM. This work demonstrates that integrating DOB-based compensation with GA-optimized control enhances robustness and 3D trajectory tracking in TDCMs. Future work will extend the framework to account for distributed external forces along the manipulator body and explore adaptive or learning-based controllers for real-time uncertainty compensation.

In this paper, we propose a novel unified framework for virtual guides. The human–robot interaction is based on a virtual robot, which is controlled by the admittance control. The unified framework combines virtual guides, control of the dynamic behavior, and path tracking. Different virtual guides and active constraints can be realized by using dead-zones in the position part of the admittance controller. The proposed algorithm can act in a changing task space and allows selection of the tasks-space and redundant degrees-of-freedom during the task execution. The admittance control algorithm can be implemented either on a velocity or on acceleration level. The proposed framework has been validated by an experiment on a KUKA LWR robot performing the Buzz-Wire task.

Consider the practically relevant situation in which a robotic system is assigned a task to be executed in an environment that contains moving obstacles. Generating collision-free motions that allow the robot to execute the task while complying with its control input limitations is a challenging problem, whose solution must be sought in the robot state space extended with time. We describe a general planning framework which can be tailored to robots described by either kinematic or dynamic models. The main component is a control-based scheme for producing configuration space subtrajectories along which the task constraint is continuously satisfied. The geometric motion and time history along each subtrajectory are generated separately in order to guarantee feasibility of the latter and at the same time make the scheme intrinsically more flexible. A randomized algorithm then explores the search space by repeatedly invoking the motion generation scheme and checking the produced subtrajectories for collisions. The proposed framework is shown to provide a probabilistically complete planner both in the kinematic and the dynamic case. Modified versions of the planners based on the exploration–exploitation approach are also devised to improve search efficiency or optimize a performance criterion along the solution. We present results in various scenarios involving non-holonomic mobile robots and fixed-based manipulators to show the performance of the planner.

This paper presents a dynamic-level control algorithm to meet simultaneously multiple desired tasks based on allocated priorities for redundant robotic systems. It is shown that this algorithm can be treated as a general framework to achieve control over the whole body of the robot. The control law is an extension of the well-known acceleration-based control to the redundant robots, and considers also possible interactions with the environment occurring at any point of the robot body. The stability of this algorithm is shown and some of the previously developed results are formulated using this approach. To handle the interaction on robot body, null space impedance control is developed within the multi-priority framework. The effectiveness of the proposed approaches is evaluated by means of computer simulation.

A new mathematical formulation of robot and obstacles is presented such that for on-line collision recognition only robot joint positions in workspace are required. This reduces calculation time essentially because joint positions in workspace can be computed every time from the joint variable through robot geometry. It is supposed that the obstacles in the workspace of the manipulator are represented by convex polygons. For every link of the redundant robot and every obstacle a boundary ellipse in 2D is defined in workspace such that there is no collision if the robot joints are outside these ellipses. First, some methods are presented for the automatic determination of these ellipse functions from the obstacle and robot data. Then, the boundary ellipse functions are used as optimization criterion in a collision-avoidance method. The method permits the tip of the hand to follow a given path in the free space while the kinematic control algorithm maximizes the boundary ellipse function of the critical link. The effectiveness of the proposed methods is discussed by theoretical considerations and illustrated by simulations of the motion of three- and four-link manipulators between obstacles.

Multilink robot arms are geometrically similar to chain molecules. We investigate the performance of molecular simulation methods, combined with stochastic methods for optimization, when applied to problems of robotics. An efficient and flexible algorithm for solving the inverse kinematic problem for redundant robots in the presence of obstacle's (and other constraints) is suggested. This “Constrained Kinematics/Stochastic Optimization” (CKSO) method is tested on various standard problems.

A new mathematical formulation of robot and obstacles is presented such that for on-line collision recognition only robot joint positions in the workspace are required. This reduces calculation time essentially because joint positions in workspace can be computed every time from the joint variables through robot geometry. It is assumed that the obstacles in the workspace of the manipulator are represented by convex polygons. For every link of the redundant robot and every obstacle a boundary ellipse is defined in workspace such that there is no collision if the robot joints are outside this ellipsis.

In addition to this, a collision avoidance method is presented which allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effector trajectory. The method is based on the generalized inverse with boundary ellipse functions as optimization criteria. The method permits the tip of the hand to approach any arbitrary point in the free space while the kinematic control algorithm maximizes the boundary ellipse function of the critical link. The effectiveness of the proposed methods is discussed by theoretical considerations and illustrated by simulations of the motion of three- and four-link planar manipulators between obstacles.

In this paper two explicit force control schemes for underwater vehicle-manipulator systems are presented. The schemes take into account several factors such as uncertainty in the model knowledge, presence of hydrodynamic effects, kinematic redundancy of the system, and poor performance of vehicle's actuation system. The possible occurrence of loss of contact due to vehicle's movement during the task is also considered, and the adoption of an adaptive motion control scheme is investigated to take advantage of dynamic compensation. The proposed control schemes have extensively been tested in numerical simulation runs; the results obtained in a case study are reported to illustrate their performance.

In some daily tasks, such as pick and place, the robot is requested to reach with its hand tip a desired target location while it is operating in its environment. Such tasks become more complex in environments cluttered with obstacles, since the constraint for collision-free movement must be also taken into account. This paper presents a new technique based on genetic algorithms (GAs) to solve the path planning problem of articulated redundant robot manipulators. The efficiency of the proposed GA is demonstrated through multiple experiments carried out on several robots with redundant degrees-of-freedom. Finally, the computational complexity of the proposed solution is estimated, in the worst case.

This paper investigates the neural network approach to solve the inverse kinematics problem of redundant robot manipulators in an environment with obstacles. The solution technique proposed requires only the knowledge of the robot forward kinematics functions and the neural network is trained in the inverse modeling manner. Training algorithms for both the obstacle free case and the obstacle avoidance case are developed. For the obstacle free case, sample points can be selected in the work space as training patterns for the neural network. For the obstacle avoidance case, the training algorithm is augmented with a distance penalty function. A ball-covering object modeling technique is employed to calculate the distances between the robot links and the objects in the work space. It is shown that this technique is very computationally efficient. Extensive simulation results are presented to illustrate the success of the proposed solution schemes. Experimental results performed on a PUMA 560 robot manipulator is also presented.