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SummaryIn this article, a solution to target convergence and obstacle avoidance problem of an underactuated nonstandard n‐trailer robot is proposed. With a new geometric approach, we propose autonomous velocity and steering angle controllers for the car‐like tractor robot such that the tractor‐trailer system moves from an initial position to a designated target. The proposed method simultaneously takes into account the dynamics constraints of the system and also ensures that the robot avoids any fixed obstacles on its way to the target. We also generalize the results to control the motion of the nonstandard n‐trailer system with an arbitrary number of passive trailers, a mathematically challenging nonlinear underactuated system, given that the angular velocity of a trailer is dependent on the angular velocity of the preceding trailer. The effectiveness of the new geometric approach and the stabilizing control inputs is verified using computer simulations.

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In this paper, we develop a planar Lagrangian swarm model using the Direct Method of Lyapunov to construct the instantaneous velocity of each individual in the swarm. The velocity controllers ensure the cohesion and therefore the stability of the swarm. We introduce novel Lyapunov functions which allow the swarm to navigate in obstacle-free and obstacle-cluttered environments. We apply the methodology to a swarm of planar nonholonomic vehicles. Via computer simulations, we illustrate several self-organizations such as parallel formation, emergent leader, split/rejoin maneuver, and tunnelling for obstacle avoidance.

Finding feasible solutions to motion planning and control problem of robotic systems in different environments with various applications is an active area of research. This article presents a new solution to the motion planning and control problem of a three-dimensional articulated mobile manipulator comprising a car-like mobile platform and a three-dimensional n-link articulated arm using the Lyapunov-based control scheme. The motion of the system is described as twofold: first, the car-like mobile platform moves from an initial position to its pseudo-target, and second, when the mobile platform is within some predefined distance from the pseudo-target, the end-effector of the robot arm is attracted to its designated target. Therefore, presenting a new 2-Step Algorithm in this paper for dual movement of the articulated mobile manipulator in 3D. In addition, a workspace cluttered with fixed spherical and rod obstacles of random sizes and positions is considered in this research. For the mobile manipulator to avoid an obstacle, the Minimum Distance Technique is adapted where a point on the robot that is closest to an obstacle will avoid the obstacle. The convergence of the two bodies and the stability of the mechanical system are guaranteed by the Lyapunov's direct method. The continuous nonlinear control laws proposed from the control scheme also take into account all mechanical singularities and velocity limitations associated with the system. Theoretical proofs and computer simulations validate the new continuous, acceleration-based, nonlinear, time-invariant control laws.