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.

Generation of high-quality drive paths is a significant issue for automated wheeled vehicles. To achieve this aim for a truck and trailer vehicle, the paper proposes the use of a parameterized curve primitive, the${\mbi \eta}^4$-spline. Using this spline, generation and shaping of smooth feasible paths is made possible as well as the transfer between arbitrary dynamic configurations of the articulated vehicle. The${\mbi \eta}^4$-spline is a ninth-order polynomial curve that can interpolate given Cartesian points with associated arbitrary unit tangent vector, curvature, and first and second derivatives of curvature. It depends on a set of eight (eta) parameters that can be freely chosen to modify the path shape without changing the interpolations conditions at the path endpoints. Completeness, minimality, and symmetry of the${\mbi \eta}^4$-spline are established. An example on a parking maneuver of the articulated vehicle is presented and the pertinent optimal path planning is also discussed.

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.