Motor actuators require accurate estimates of the velocity. When a velocity sensor is not available, the speed must be obtained by numerically differentiating the position signal. Several differentiators are proposed in the literature, all of them returning signals which are affected, at different levels, by noise and time delays. This paper proposes an alternative version of the so-called Hybrid Super Twisting Differentiator (HSTD) recently proposed in the literature. The novel HSTD, whose stability is investigated in the paper, changes its behaviour depending on the operating conditions of the system, in order to reduce noise and time delays. It is particularly suited for motor applications: as proven in the paper by means of an experimental test bench, it estimates the velocities better than alternative differentiation techniques.

Laser Guided Vehicles (LGV) are largely used in industrial contexts for the autonomous dispatching of huge loads. LGVs of automated warehouses are driven by supervisory systems which assign their tasks depending on the process demands. The vehicle workspace is partially structured and it is normally shared with several independent agents like other LGVs, or human operated forklifts, or humans which directly interact with the vehicle itself. For efficiency and for safety reasons, LGVs move along pre-defined paths so that, if an unexpected obstacle is detected, they must be promptly stopped so as to avoid impacts. As shown in the paper, the safety problem is normally handled by limiting the plant productivity. This is clearly an improper approach, which can be overcome by considering a novel velocity planning strategy. The one proposed in this paper guarantees high safety standards, thus preserving the physical integrity of human coworkers, by simultaneously improving the plant productivity.

Planning problems in the operational space are characterized by implementation issues that do not occur in the joint space. For example, depending on the manipulator pose, relatively slow trajectories in the operational space could require unfeasible joint speeds, thus causing the degeneration of the system performances: Path tracking errors certainly increase but, in the worst situations, the manipulator must be stopped in order to prevent the system instability. This paper proposes a real-time planner in the operational space that is able to generate trajectories subject to dynamic constraints and devised according to the path-velocity decomposition approach. The feasibility is achieved by means of an automatic scaling system that, starting from a possibly unfeasible trajectory, modifies its longitudinal velocity in order to fulfill a given set of kinematic constraints, thus preserving an accurate path tracking. The scaling system promptly reacts to critical configurations through minimum-time transients. The proposed approach has been tested on an actual anthropomorphic manipulator by executing 6D trajectories. Note to Practitioners - The accurate path tracking must be guaranteed especially when trajectories are planned in the operational space. Unfortunately, path tracking worsens every time system limits are exceeded. The trajectory generator proposed in this paper is specifically designed for non-redundant manipulators and it is equipped with a scaling system that automatically modifies the speed of the end effector in order to guarantee an accurate path tracking. Several kinematic constraints are handled at the same time. Joint velocities are kept below the manufacturer's limits, while joint accelerations are bounded in order to achieve smooth movements. The system is also able to constrain the kinematics of the end effector. For example, in order to reduce the mechanical stress on the payload and to avoid the excitation of elastic modes, additional bounds on the velocities and accelerations of the end effector are considered and managed. The planner can also be used to generate minimum-time constrained trajectories in real-time. To this purpose, further constraints on the longitudinal velocities and accelerations have been introduced. Differently from alternative approaches, the proposed planning scheme does not require any interaction with the controller. This is an advantage, since controllers of industrial manipulators are typically not accessible or modifiable, while, in turn, proprietary trajectory planners can normally be replaced with ad-hoc implementations. The scaling system can be easily expanded in order to handle additional constraints. The trajectory smoothness, for example, can be improved by managing the jerk bounds, so that the ongoing research activity is currently focused on that target. In the same way, it could also be possible to handle some dynamic constraints, but this would impose the introduction of mutual interactions between the scaling system and the central control unit.

User defined trajectories are often planned by neglecting the manipulator physical limits. In order to avoid stability problems and to guarantee an accurate path tracking, it is therefore necessary to equip the robot controllers with appropriate scaling mechanisms, that properly slow down assigned trajectories. In the paper, a recently proposed scaling strategy is revised in order to analyze and solve some feasibility issues that could arise on actual systems. The reliability of the proposed approach is tested against an actual 2D planar manipulator.

This paper studies an assigned-time velocity-planning problem for robotic systems that are subject to velocity and acceleration constraints. The planning problem, which is justified by several robotic applications, poses feasibility issues that are investigated in this paper. In particular, this paper shows that feasible solutions exist if and only if proper interpolating conditions are assigned, and proposes an efficient planning strategy, that is suitable for online implementations. Available degrees of freedom are used to smooth the velocity function by minimizing its maximum jerk.

Rotary encoders and resolvers are by far the most common sensors to measure joint angles in articulated robots. Since various control approaches require angular rates as well, resolvers and encoders are also employed to derive angular rate signals. Due to the involved differentiation operation, however, quantization noise may be augmented significantly. Advanced filtering approaches can only partially overcome this drawback. Therefore, direct measurement of angular rates is desirable. Due to advancements in manufacturing technology and pushed by applications in entertainment devices, MEMS gyroscopes have become an attractive alternative for angular rate measurement. Unfortunately, they are affected by bias and other non-negligible disturbances, which may be a serious problem if consistent joint angle and angular rate measurements are required. The proposed approach fuses encoder and angular rate signals to mitigate their major drawbacks - bias and quantization errors - by exploiting their individual strong points. Bias in the angular rate signal is eliminated by analyzing the deviation between the integrated angular rate signal and the encoder signal. Quantization errors in the encoder signal are reduced by a so-called complementary filter which blends the integrated angular rate output with the encoder signal. Apart from a description of the approach and a theoretical analysis of its characteristics, experimental results demonstrating the effectiveness of the approach in closed-loop control of articulated robots are presented.

Online trajectory scaling approaches represent a possible way for handling robotic systems characterized by kinematic or dynamic saturations. Scaling methods are based on the path/velocity decomposition principle: a dynamic filter is used to modify the longitudinal velocity along a planned path in order to satisfy given system constraints. The strategy here proposed enhances the results of a previous work by enlarging the number of considered constraints. In particular, still accounting for the existence of bounds on joint velocities and torques, in this paper, the presence of constraints on joint accelerations is also considered. Furthermore, the nonlinear filter, which represents the core of the scaling system, has been revised in order to devise a new and more compact implementation. Finally, some practical issues that could occur in actual implementations are discussed and solutions are proposed to overcome possible problems.

Robotic manipulators are usually driven by means of minimum-time trajectories. Unfortunately, such trajectories strongly solicit the actuators whose dynamic limits could be easily exceeded. Therefore, kinematic and/or dynamic constraints are commonly considered for offline planning. Nevertheless, during actual operations, dynamic limits could be violated because of model uncertainties and measurement noise, thus causing performance losses. In order to fulfill the given bounds with certainty, planned trajectories are typically online scaled, by accounting for generalized force (GF) constraints. The resulting command signal is typically discontinuous; therefore, the system mechanics are unnecessarily solicited, and nonmodeled dynamics are excited. Moreover, in the case of systems that admit limited derivatives for GFs, tracking accuracy worsens. To prevent possible problems that derive from GF discontinuities, this paper proposes an online trajectory scaling approach that accounts for the simultaneous existence of joint constraints on GFs and their derivatives. At the same time, it is able to manage bounds on joint velocities, accelerations, and jerks.

The performances of controlled systems can be improved by driving them with smooth reference signals. In case of rough signals, smoothness can be achieved with the help of appropriate dynamic filters. To this purpose a novel discrete-time filter is proposed in the paper. It has been appositely designed for real-time motion applications like those that can be encountered in robotic or mechatronic contexts. The filter generates output signals which are continuous together with their first and second time derivatives. Simultaneously, the first, the second, and the third time derivatives are bounded within freely assignable limits. If such limits are changed on-the-fly, the filter hangs the new bounds in minimum-time. An example case shows the filter while tracking steps, ramps and parabolas by means of bounded-dynamic transients.

This paper deals with the generation of smooth paths planned by means of$ { \mmb{\eta } }^{3}$-splines, a recently devised planning primitive used for the automated steering of wheeled mobile robots. The shape of$ { \mmb{\eta } }^{3}$-splines can be easily modified by acting on a set of free parameters. This capability can be used, for example, to satisfy an assigned optimality criterion. In this paper, it will be used to minimize the curvature variability in order to reduce the lateral solicitations affecting an autonomous robot. Evidently, curvature derivative could be minimized by means of an optimization algorithm. However, this approach cannot be suitably used in an online application which continuously requires the curve updating. For this reason, a heuristic method, based on closed form expressions, has been devised and proposed in the paper in order to efficiently generate almost optimal curves on the sole basis of the interpolating conditions. As a further characteristic, the proposed heuristic expressions permit obtaining, when appropriate interpolating conditions are given,$ { \mmb{\eta } }^{3}$-splines which at best emulate circular arcs and clothoids.

The behaviour of robotic manipulators is affected by the actuators dynamic limits. When such limits are not explicitly considered, manipulators performances rapidly decrease. In this paper, dynamic saturations are handled by means of a real-time technique based on a trajectory scaling method: whenever saturations occur, trajectories are automatically scaled by means of a dynamic filter in order to preserve an accurate path tracking. Commonly known scaling algorithms only consider the existence of torque saturations. In this paper, the strategy is enriched by also accounting for torque derivatives constraints. The solution proposed is suited to be used in conjunction with standard inverse dynamics controllers. The adopted methodology explicitly requires the realtime evaluation of the derivative of the manipulator inertia matrix. To this purpose, a novel efficient procedure is proposed.

An accurate estimation of the dynamics efforts acting on a robot manipulator represents an important issue for both the analysis of its behavior and the synthesis of appropriate controllers. This paper proposes an iterative algorithm, which is based on the Newton–Euler approach, for the efficient evaluation of the manipulators' high-order kinematics and dynamics. In particular, the algorithm computes velocities, accelerations, and jerks of each link, while new dynamic equations are devised in order to evaluate the first derivative of generalized forces. Due to its moderate computational burden, the algorithm is suited to be used in online applications.

Modeling of traction forces generated by wheels is a problem which is being investigated by many years. Several models have been proposed whose complexity depends on the desired accuracy. An evergreen model, which is very often cited and used, is the one proposed by Dugoff et al. in 1970. Despite its simplicity it returns a very good characterization of the phenomena acting on a wheel and has the undoubt advantage of being obtained on the basis of physical considerations. In this paper the original model is revised in order to solve some inconsistencies. Two models have been proposed where the variables conventionally used to characterize the wheel forces, i.e., slip s and side slip alpha, are replaced with a new vectorial variable. A more accurate estimate of the wheel forces has been obtained by removing one simplifying approximation of the original model. Comparisons are proposed between the Dugoff model and the new models.

Minimum-time path-tracking control of robotic manipulators assumes a relevant role in industrial applications where efficiency is an issue. On the other hand, minimizing the traveling time leads to an increment of the mechanical solicitations: the actuators dynamic limits can be easily exceeded. For this reasons, kinematic and/or dynamic constraints are normally taken into account when planning optimal trajectories through off-line algorithms. Nevertheless this precaution, dynamic limits can be easily violated during actual operations due to model uncertainties and the action of the feedback controller. In order to fulfill with certainty the given constraints, planned trajectories are typically online scaled by means of dynamic filters. Normally, this is done by only considering torque constraints. On the contrary, in this paper, the trajectory is online scaled by also taking into account the existence of bounds on the torque derivatives. Indeed, torque derivatives have a direct impact both on the mechanical solicitations and on the tracking accuracy. A new nonlinear filter is proposed for the optimal trajectory scaling. Its effectiveness is verified by means of simulations.

The paper addresses a velocity planning problem for autonomous vehicles. Appropriate bounds on velocities and accelerations have to be considered in order to avoid wheels skidding and actuators saturation. Planned profiles fulfill an assigned travelling time, while longitudinal jerk is minimized in order to increase the motion smoothness. In the paper it is shown that the velocity planning problem can be formulated as a nonlinear semi-infinite optimization to be solved in real time by means of an appositely devised algorithm characterized by a light computational burden.

The paper proposes a linear programming approach to the feedforward minimum-time control of flexible joints. Taking into account both input and output constraints, the optimal bang-bang control is computed by discretizing a continuous-time joint model and by solving a sequence of linear programming feasibility problems. The resulting joint motion is a smooth rest-to-rest motion without oscillations. Experimental results illustrate the proposed open-loop technique.

The paper deals with the generation of smooth paths for the inversion-based motion control of wheeled mobile robots. A new path primitive, called$ { \mmb{\eta } }^{3}$-spline, is proposed. It is a seventh order polynomial spline which permits the interpolation of an arbitrary sequence of points with associated arbitrary tangent directions, curvatures, and curvature derivatives, so that an overall$\mmb G^{3}$-path is planned. A$\mmb G^{3}$-path or path with third order geometric continuity has continuous tangent vector, curvature, and curvature derivative along the arc length. Adopting this planning scheme and a dynamic path inversion technique, the robot's command velocities are continuous with continuous accelerations. The new primitive depends on a vector ($ { \mmb{\eta } }$) of six parameters that can be used to finely shape the path. The$ { \mmb{\eta } }^{3}$-spline can generate or approximate, in a unified framework, a variety of curve primitives such as circular arcs, clothoids, spirals, etc. The paper includes theoretical results, path planning examples, and a note on general$ { \mmb{\eta } }^{k}$-splines.

The path-velocity decomposition scheme is frequently adopted in the context of trajectory planning. A technique for the optimal velocity planning, to be used that framework, is proposed in this paper. Differentiable velocity profiles, which fulfil assigned initial and final boundary conditions on the velocity itself and on its first derivative, are obtained by means of the proposed strategy. Moreover, profiles are constrained between assigned bounds, i.e. velocity is limited, and its second derivative (the longitudinal jerk) is minimized by means of an optimization algorithm. The extensive use of closed form expressions makes this approach suitable to be implemented in real-time applications.

A new motion-generation approach is proposed for wheeled mobile robots described by the unicycle kinematic model. This approach permits the generation of smooth continuous-acceleration controls using a dynamic path-inversion procedure that exploits the concept of G/sup 3/ -paths, i.e., Cartesian paths with third-order geometric continuity (both the curvature function and its derivative, with respect to the arc length, are continuous). The exposed steering method is well suited to be adopted for the robot's iterative steering within a supervisory control architecture for sensor-based autonomous navigation. A worked example illustrates the approach.

This paper presents a new motion planning primitive to be used for the iterative steering of vision-based autonomous vehicles. This primitive is a parameterized quintic spline, denoted as /spl eta/-spline, that allows interpolating an arbitrary sequence of points with overall second-order geometric (G/sup 2/-) continuity. Issues such as completeness, minimality, regularity, symmetry, and flexibility of these G/sup 2/-splines are addressed in the exposition. The development of the new primitive is tightly connected to the inversion control of nonholonomic car-like vehicles. The paper also exposes a supervisory strategy for iterative steering that integrates feedback vision data processing with the feedforward inversion control.

Presents the methods for sensing obstacles and vehicles implemented on the University of Parma experimental vehicle (ARGO). The ARGO project is briefly described along with its main objectives; the prototype vehicle and its functionalities are presented. The perception of the environment is performed through the processing of images acquired from the vehicle. Details about the stereo vision-based detection of generic obstacles are given, along with a measurement of the performance of the method; then a new approach for leading vehicles detection is described, relying on symmetry detection in monocular images. The paper concludes with a description of the current implementation of the control system, based on a gain scheduled controller, which allows the vehicle to follow the road or other vehicles.

A direct drive variable reluctance motor for robotic applications is considered. A cascade control structure is adopted, with an inner torque loop and an outer velocity loop. The inner loop consists of a static torque precompensator transforming the torque control problem into a current or flux control one. Optimization techniques that minimize power dissipation under the voltage limit imposed by the power amplifier are used to define an optimal ripple-free flux profile. Sliding mode implementation of the inner controller is considered, while the outer loop is designed using binary control techniques to achieve insensitivity to load and inertia variations. The drive is simulated for a single-link robotic arm, showing good performances in terms of residual torque ripple and velocity-tracking capability.>