Oscar Gerelli

Nonlinear Variable Structure Filter for the Online Trajectory Scaling

Time efficiency and accurate path tracking represent two conflicting demands typical of robotic applications: Time efficiency induces one to plan extremely fast trajectories which can easily collide with the manipulator kinematic and dynamic constraints, thus causing a reduction of accuracy. To deal with this problem, several approaches can be found in the literature mainly based on the synthesis of dynamic filters used for the online trajectory scaling: A possibly unfeasible input trajectory is automatically scaled to fulfill given dynamic bounds. In this way, an accurate path tracking is guaranteed. This paper can be collocated in such a framework. A new discrete-time filter, with novel capabilities, is designed. Differently from other proposals, not only torque constraints are considered but also kinematic constraints are easily handled. Moreover, to preserve time efficiency, the new filter always attempts to recover any delay caused by the constraints.

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.

Generation of Paths With Minimum Curvature Derivative With

This paper deals with the generation of smooth paths planned by means of η3-splines, a recently devised planning primitive used for the automated steering of wheeled mobile robots. The shape of η3-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, η3-splines which at best emulate circular arcs and clothoids.

{ \mmb{\eta } }^{3}

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.

-Splines

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.

Real-time path-tracking control of robotic manipulators with bounded torques and torque-derivatives

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.

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

In this paper, we analyze in depth the innovative very versatile and energy efficient (V2E2) actuator proposed in Stramigioli et al. (2008). The V2E2 actuator is intended to be used in all kind of robotics and powered prosthetic applications in which energy consumption is a critical issue. In particular, this work focuses on the development of a port-based Hamiltonian model of the V2E2 and presents an optimal control architecture which exploits the intrinsic hybrid characteristics of the actuator design. The optimal control guarantees the minimization of dissipative power losses during torque tracking transients.

Minimum-time control of flexible joints with input and output constraints

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.

Port-based modeling and optimal control for a new very versatile energy efficient actuator

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 alternative model for the evaluation of tyre shear forces under steady-state conditions

Starting from Pontryagins maximum principle (PMP), a geometric approach is presented in order to find the optimal control for dynamic systems with input constraints. The proposed algorithm works in the cases in which the reachable sets are convex. The approach is based on the PMP for which, in some cases, optimal solution can be generated with the knowledge of two parameters: the transition time, t*, and the final costate, q1, which is the normal vector to the boundary of the set reachable at time t* at the final state. The devised algorithm is able to find the right values of t* and q1 that guarantee to reach the final state x1, through a geometric method that makes use of the convexity of system reachable sets. A convergence analysis is presented and the method is validated through simulations and experiments on three sample systems: a double order integrator, a mass on a cart, for which the reachable set is also represented, and the linearized model of a flexible joint device.