Corrado Guarino Lo Bianco

Minimum-time trajectory planning of mechanical manipulators under dynamic constraints

The paper presents a global optimization approach to the trajectory planning problem of mechanical manipulators. The purpose is to obtain a minimum-time cubic spline trajectory subject to constraints given by limited joint torques and torque derivatives taking into account the non-linear manipulator dynamics. It is shown how, without conservativeness, a semi-infinite optimization problem emerges. Conditions ensuring that the formalized problem admits a solution are given. The estimated global solution can be actually obtained by means of an hybrid genetic/interval algorithm that guarantees the feasibility of the found solution. The methodology is illustrated with numerical details for a two-link planar arm and a PUMA six-link manipulator; for the former, comparisons with an alternative optimization solver are exposed.

A hybrid algorithm for infinitely constrained optimization

Infinitely constrained (or semi-infinite) optimization can be successfully used to solve a significant variety of optimization-based engineering design problems. In this paper a new algorithm for the numerical global solution of nonlinear and nonconvex, infinitely constrained problems is proposed. At the upper level this hybrid algorithm is a partially elitist genetic algorithm that uses, at the lower level, an interval procedure to compute a penalty-based fitness function. The deterministic nature of the interval procedure, whose global convergence with certainty is established by using concepts of interval analysis, guarantees the feasibility of the estimated global solution provided by the hybrid algorithm. Computational results are reported for three test problems and the hybrid algorithm is applied to the optimal worst-case H2 design of a proportionalintegral-derivative (PID) controller for an uncertain nonminimum-phase plant.

A servo control system design using dynamic inversion

Abstract This paper presents an inversion-based approach to the design of a dc motor-position servo system. Specifically, using the recently developed transition polynomials, a dynamic inversion procedure is established to determine a feedforward command signal to achieve high-performance position transfers. It is shown how to improve a traditional proportional and derivative controller feedback scheme and how a coordinated feedforward/feedback design using the new approach further improves the servo performances. Moreover, the methodology can easily comply with a voltage saturation avoidance constraint. Experimental results on a standard test bench highlight the effectiveness of the dynamic inversion idea.

Online Trajectory Scaling for Manipulators Subject to High-Order Kinematic and Dynamic Constraints

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.

A Semi-Infinte Optimization Approach to Optimal Spline Trajectory Planning of Mechanical Manipulators

The paper deals with the problem of optimal trajectory planning for rigid links industrial manipulators. According with actual industrial requirements, a technique for planning minimum-time spline trajectories under dynamics and kinematics constraints is proposed. More precisely, the evaluated trajectories, parametrized by means of cubic splines, have to satisfy joint torques and end-effector Cartesian velocities within given bounds. The problem solution is obtained by means of an hybrid genetic/interval algorithm for semi-infinite optimization. This algorithm provides an estimated global minimizer whose feasibility is guaranteed by the use of a deterministic interval procedure; i.e., a routine based on concepts of interval analysis. The proposed approach is tested by planning a 10 via points movement for a two link manipulator.

A discrete-time filter for the on-line generation of trajectories with bounded velocity, acceleration, and jerk

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.

Minimum-Jerk Velocity Planning for Mobile Robot Applications

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.

Real-Time Planner in the Operational Space for the Automatic Handling of Kinematic Constraints

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 manufacturers 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.

A Discrete-Time Filter for the Generation of Signals With Asymmetric and Variable Bounds on Velocity, Acceleration, and Jerk

Reference signals, which are used to drive feedback control loops, are often evaluated on the fly on the basis of the operating conditions. As a consequence, they can be too demanding for the actuation system whose outputs could saturate, thus worsening the tracking performances of the feedback loop. Improved answers can be obtained by smoothing rough references by means of proper filters that are also able to impose bounds on the signal dynamics. This paper proposes a filtering system whose output mimics at best any given input signal compatibly with some smoothness requirements. In particular, generated signals are continuous up to the second time derivative, and their first three time derivatives are constrained between assigned bounds that can be asymmetric and that can also be changed on the fly. The filter, which is internally characterized by minimum time transients, is able to follow, with zero tracking error, piecewise-continuous signals given by combinations of steps, ramps, and parabolas.

A novel second order filter for the real-time trajectory scaling

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.