The time-optimal path problem for a point mass mobile robot is considered. Given initial and target states, we seek the time optimal path subject to the following constraints: (1) A limitation on its maximal linear acceleration; (2) a speed-dependent nonsliding condition; and (3) a minimal radius of turn. The paper formulates and analyzes the time optimal path problem using standard optimal control formulation with extensive use of the classical Hodograph method. Based on the analysis, the time optimal path consists of five path primitives. Numerical solutions are obtained to support and illustrate the analysis.

This paper addresses the problem of goal-directed robot path planning in the presence of uncertainties that are induced by bounded environmental disturbances and actuation errors. The offline infinite-horizon optimal plan is locally updated by online finite-horizon adaptive replanning upon observation of unexpected events (e.g., detection of unanticipated obstacles). The underlying theory is developed as an extension of a grid-based path planning algorithm, called ν⋆, which was formulated in the framework of probabilistic finite state automata (PFSA) and language measure from a control-theoretic perspective. The proposed concept has been validated on a simulation test bed that is constructed upon a model of typical autonomous underwater vehicles (AUVs) in the presence of uncertainties.

First-excursion times have been developed extensively in the literature for oscillators; one major application is structural dynamics of buildings. Using the fact that most closed-loop systems operate with a moderate to high damping ratio, we have derived a new procedure for calculating first-excursion times for a class of linear continuous, time-varying systems. In several examples, we show that the algorithm is both accurate and time-efficient. These are important attributes for real-time path planning in stochastic environments, and hence the work should be useful for autonomous robotic systems involving marine and air vehicles.

We propose a framework for synthesizing real-time trajectories for a wide class of coordinating multi-agent systems. The class of problems considered is characterized by the ability to decompose a given formation objective into an equivalent set of lower dimensional problems. These include the so called radar deception problem and the formation control problems that fall under formation keeping and/or formation reconfiguration tasks. The decomposition makes the approach scalable, computationally economical, and decentralized. Most importantly, the designed trajectories are dynamically feasible, meaning that they maintain the formation while satisfying the nonholonomic and saturation type velocity and acceleration constraints of each individual agent. The main contributions of this paper are (i) explicit consideration of second order dynamics for agents, (ii) explicit consideration of nonholonomic and saturation type velocity and acceleration constraints, (iii) unification of a wide class of formation control problems, and (iv) development of a real-time, distributed, scalable, computationally economical motion planning algorithm.

In this paper, time optimal trajectory tracking of redundant planar cable-suspended robots is investigated. The equations of motion of these cable robots are obtained as a system of second order differential equation in terms of path parameter s using the specified path. Besides, the bounds on the cable tensions and cable velocities are transformed into the bounds on the acceleration and velocity along the path. Assuming bang-bang control, the switching points in s ̇ 2 − s plane are obtained. Then the cable tensions are found in terms of path parameter and, subsequently, versus time. The proposed approach is validated and the effect of the number of superfluous cables on the value of minimum time is studied. The next notable challenges include time optimal path planning of cable-suspended robots. By developing a hybrid genetic algorithm and bang-bang control approach, the minimum motion time from initial state to final one and also the corresponding path can be found. The optimum path is the one that minimizes traveling time from initial state to final one, while not exceeding the cable tensions and cable velocities limits, without collision with any obstacles.

This paper presents the application of advanced optimization techniques to unmanned aerial system mission path planning system (MPPS) using multi-objective evolutionary algorithms (MOEAs). Two types of multi-objective optimizers are compared; the MOEA nondominated sorting genetic algorithm II and a hybrid-game strategy are implemented to produce a set of optimal collision-free trajectories in a three-dimensional environment. The resulting trajectories on a three-dimensional terrain are collision-free and are represented by using Bézier spline curves from start position to target and then target to start position or different positions with altitude constraints. The efficiency of the two optimization methods is compared in terms of computational cost and design quality. Numerical results show the benefits of adding a hybrid-game strategy to a MOEA and for a MPPS.

This paper deals with visual servoing for 6-degree-of-freedom robot manipulators, and considers the problem of establishing whether and how it is possible to reach the desired location while keeping all features in the field of view and following a straight line in the Euclidean space. A path-planning technique based on a parametrization of the camera path through polynomials is proposed, which overcomes existing methods dealing with this problem. The generated image trajectory can be tracked by using an image-based visual servoing controller.

Safe and simultaneous arrival of constant speed, constant altitude unmanned air vehicles (UAVs) on target is solved by design of paths of equal lengths. The starting point for our solution is the well-known Dubins path, which is composed of circular arc and line segments, thus requiring only one simple maneuver—constant rate turn. An explicit bound can be imposed on the rate during the design and the resulting paths are the minimum time solution of the problem. However, transition between arc and line segments entails discontinuous changes in lateral acceleration (latax), making this approach impractical for real fixed wing UAVs. Therefore, we replace the Dubins solution with a novel one, based on quintic Pythagorean hodograph (PH) curves, whose latax demand is continuous. The PH paths are designed to have lengths close to the lengths of the Dubins paths to stay close to the minimum time solution. To derive the PH paths, the Dubins solution is first interpreted in terms of differential geometry of curves using the path length and curvature as the key parameters. The curvature of a Dubins path is a piecewise constant and discontinuous function of its path length, which is a differential geometric expression of the discontinuous latax demand involved in transitions between the arc and the line segment. By contrast, the curvature of the PH path is a fifth order polynomial of its path length. This is not only continuous but also has enough design parameters (polynomial coefficients) to meet the latax (curvature) constraints (bounds) and make the PH solution close to the minimum time one. The solution involves the design of paths meeting the curvature constraint and is followed by producing multiple paths of equal length by increasing the lengths of the shorter paths to match the longest one. The safety constraint, intercollision avoidance is achieved by satisfying two conditions: minimum separation distance and nonintersection at equal distance. The offset curves of the PH path are used to design a safety region along each path.

The control of networked multivehicle systems designed to perform complex coordinated tasks is currently an important and challenging field of research. This paper addresses a cooperative search problem where a team of uninhabited aerial vehicles (UAVs) seeks to find targets of interest in an uncertain environment. We present a practical framework for online planning and control of a group of UAVs for cooperative search based on two interdependent tasks: (i) incrementally updating “cognitive maps” used as the representation of the environment through new sensor readings; (ii) continuously planning the path for each vehicle based on the information obtained through the search. We formulate the cooperative search problem and develop a decentralized strategy based on an opportunistic cooperative learning method, where the emergent coordination among vehicles is enabled by letting each vehicle consider other vehicles’ actions in its path planning procedure. By using the developed strategy, physically feasible paths for the vehicles to follow are generated, where constraints on aerial vehicles, including physical maneuverabilities, are considered and the dynamic nature of the environment is taken into account. We also present some mathematical analysis of the developed search strategy. Our analysis shows that this strategy guarantees a complete search of the environment and is robust to a partial loss of UAVs. A lower bound on the search time for any strategy and a relaxed upper bound for the proposed strategy are given. Simulation results are used to illustrate the effectiveness of the proposed strategy.

In this paper we propose a sliding-mode antiswing control for overhead cranes. The objective of this study is to realize an antiswing trajectory control with high-speed load hoisting. A sliding-mode antiswing trajectory control scheme is designed based on the Lyapunov stability theorem, where a sliding surface, coupling the trolley motion with load swing, is adopted for a direct damping control of load swing. The proposed control guarantees asymptotic stability while keeping all internal signals bounded. In association with a new antiswing motion planning scheme, the proposed control realizes a typical antiswing trajectory control in practice, allowing high-speed load-hoisting motion and sufficient damping of load swing. The proposed control is simple for a real-time implementation with high-frequency sampling. The effectiveness of the proposed control has been confirmed by experiments.

We consider the problems of kinematic and dynamic constraints, with actuator saturation and wheel slippage avoidance, for motion planning of a holonomic three-wheeled omni-directional robot. That is, the motion planner must not demand more velocity and acceleration at each time instant than the robot can provide. A new coupled non-linear dynamics model is derived. The novel concepts of Velocity and Acceleration Cones are proposed for determining the kinematic and dynamic constraints. The Velocity Cone is based on kinematics; we propose two Acceleration Cones , one for avoiding actuator saturation and the other for avoiding wheel slippage. The wheel slippage Acceleration Cone was found to dominate. In practical motion, all commanded velocities and accelerations from the motion planner must lie within these cones for successful motion. Case studies, simulations, and experimental validations are presented for our dynamic model and controller, plus the Velocity and Acceleration Cones .

The precise control of a manipulator depends on its velocity as well as on its configuration and dynamic properties. This paper presents some observations that can serve as a useful tool for identifying nonlinear ear effects in a manipulator. The tool is based on equations of motion being expressed in terms of inertial quasi-velocities (IQVs). They are rates containing both kinematic and mechanical parameters of the system. The presented approach gives a further insight into the manipulator motion. An analytical example shows the proposed strategy.

This paper presents a practical method for automatic tip-over prevention and path following control of a redundant nonholonomic mobile modular manipulator. According to modular robot concept, the mobile platform is treated as a special module attached to the base of the modular manipulator, then an integrated structure is constructed and its dynamic modeling is performed. A new tip-over stability criterion based on the supporting forces is proposed in consideration of inertia, gravity, and acceleration. An online fuzzy logic (FL) self-motion planner and an adaptive neural-fuzzy controller (ANFC) are presented: The former is used to generate desired self-motions in a real-time manner, and the latter is used to prevent the robot from tipping over and to control the end-effector to follow a desired spacial trajectory at the same time. The proposed algorithm does not need any a priori knowledge of dynamic parameters and can suppress bounded external disturbances effectively. Simulation results for a real robot validate the dynamic modeling method and the controller design algorithm.

In this paper, a general framework for trajectory planning and tracking is formulated for dynamically stabilized mobile systems, e.g., inverted wheeled pendulums and autonomous helicopters. Within this framework, the system state is divided into slow and fast substates. The fast substate is used as a pseudocontrol for tracking a desired slow substate trajectory. First, an exponential fast substate controller is designed to track a fast substate reference trajectory. This fast substate reference trajectory is, in turn, planned so that the slow substate follows its desired trajectory. To ensure that the fast substate reference trajectory is feasible for the exponential controller, it is designed using band-limited “Sinc” functions whose maximum frequency is less than the inverse of the time constant of the exponential controller. To illustrate the procedure, the dynamic model of an inverted wheeled pendulum is reformulated by a partial feedback linearization such that it is amenable to the separation into slow and fast components. The planning and tracking controller design is explained using simulation results. This technique is shown to be easily embedded inside a modified nonlinear model predictive control framework for the slow subsystem. This framework tries to explicitly take the computational delay into account. The computation time required for this technique is encouraging from a real-world implementation perspective.

Ground autonomous mobile robots have important applications, such as reconnaissance, patrol, planetary exploration, and military applications. In order to accomplish tasks on rough terrain, control and planning methods must consider the physical characteristics of the vehicle and of its environment. Failure to understand these characteristics could lead to vehicle endangement and consequent mission failure. This paper describes recent and current work at the Politecnico of Bari in collaboration with the University of Lecce in the area of deformable terrain mobility and sensing. A cylindrical mobile robot is presented and its rolling motion on terrain is studied from a theoretical and experimental prospect. A comprehensive model is developed taking into account the interaction of the vehicle with the terrain and the related dynamic ill effects, such as rolling resistance and slip, and it is experimentally validated. An unconventional application of the vehicle serving as a tactile sensor is discussed and experimental results are presented showing the effectiveness of the cylindrical mobile robot in estimating the properties of homogeneous, deformable terrain, which in turn can be used to assess the vehicle traversability.

Passive robotic devices may exhibit a spatially varying apparent inertia perceptible to a human user. The apparent inertia is the projection of the inertia matrix onto the instantaneous direction of motion. The spatial variation is due to the configuration dependence of the inertia matrix and relevant to many passive mechanisms, including programmable constraint machines or “cobots,” which use low-power steering actuators to choose the direction of motion. We develop two techniques for controlling the apparent inertia in cobots to emulate the desired inertial properties of a virtual object or mechanism. The first is a path-limiting method, which constraints the cobot to steer along certain paths where the apparent inertia and desired inertia are equivalent. The second uses a low-power actuator to control the apparent inertia by driving the device along its direction of motion. We illustrate these ideas for a two-link cobot we have built for experiments in human motor control and rehabilitation. For the actuated control method, we show that the power actuator can be relatively low power compared to the actuators of a traditional robot performing similar tasks.

Parallel manipulators are uncontrollable at force singularities due to the infeasibly high actuator forces required. Existing remedies include the application of actuation redundancy and motion planning for singularity avoidance. While actuation redundancy increases cost and design complexity, singularity avoidance reduces the effective workspace of a parallel manipulator. This article presents a path tracking type of approach to operate parallel manipulators when passing through force singularities. We study motion feasibility in the neighborhood of singularity and conclude that a parallel manipulator may track a path through singular poses if its velocity and acceleration are properly constrained. Techniques for path verification and tracking are presented, and an inverse dynamics algorithm that takes actuator bounds into account is examined. Simulation results for a planar parallel manipulator are given to demonstrate the details of this approach.

This paper describes a prototype and analytical studies of a spherical rolling robot, a new design of an omnidirectional robot system. The robot can arbitrarily begin to move in any direction to the target, and autonomously roll and reach any desired position. Our design has considered a spherical robot with an internal mechanism for propulsion. The propulsion mechanism will distribute weights radially along spokes fixed inside the sphere and enables the robot to accelerate, decelerate, and move with constant velocity. A mathematical model of the robot’s dynamic and motion was instructed. An algorithmic motion planning is developed and, partly, pseudocode of that is presented. For a number of missions, it is shown experimentally that the model agrees well with the results.

This paper proposes a motion-planning method for a high-performance anti-swing control of overhead cranes, where the motion-planning problem is solved as a kinematic problem. First, an anti-swing regulating control law is proposed based on the Lyapunov stability theorem, where the proposed anti-swing control drives trolley velocity regulating error asymptotically to zero while suppressing load swing rapidly to zero for given arbitrary high-speed hoisting motions. Then a motion-planning scheme is designed based on the concept of minimumtime control, the proposed anti-swing control law, and typical anti-swing crane-operation practices. The motion-planning scheme is free from the usual mathematical constraints in anti-swing control such as small swing angle, small hoisting speed, and small hoisting distance. The effectiveness of the proposed motion planning is shown by generating high-performance anti-swing trajectories with high hoisting speed and hoisting ratio.

In this work is considered the problem of rest-to-rest motion in a desired pre-fixed time for planar flexible manipulators. We introduce a simple idea permitting the minimization of end-effector residual vibration when reaching a desired angular equilibrium position, in a pre-fixed desired travelling time. The results hold without considering internal elastic damping effect , using a classical controller with feedforward plus joint feedback terms . The new approach concerns the computation of the feedforward control, which is based on backward integration of the elastic dynamics, starting from a rest position of the flexible arms. This backward integration yields basically elastic trajectories permitting to reach the final desired end-effector position without oscillation. The feedback controller is then used to stabilize locally the actual states along these desired trajectories. However, for fast rest to rest motion, the feedback compensator fails to drive the system states along the desired trajectories, this being due to the relatively large initial elastic error. To overcome this limitation, proper joint motion is planned between the desired initial and final positions through optimization techniques, the goal being the minimization of the initial elastic error associated to these joint trajectories. The optimal planning technique is formulated as a Pontryagin optimal control problem. This scheme is validated via numerical tests as well as experiments on a flexible two-link planar manipulator.