Wannes Van Loock

Experimental validation of nonlinear MPC on an overhead crane using automatic code generation

Recent advances in improving the efficiency of nonlinear model predictive control (MPC) algorithms have made them suited for challenging mechatronic applications that require high sampling rates. We demonstrate this fact by applying a highly efficient nonlinear MPC algorithm to a laboratory-scale overhead crane setup, featuring a fast moving cart and a winch mechanism. The aim is to perform optimized point-to-point motions with varying line length while respecting actuator limits. In order to solve the resulting optimization problems in less than one millisecond, an automatically generated Gauss-Newton real-time iteration algorithm is employed. We show experimental results illustrating the control performance of the closed-loop system as well as the efficiency of the nonlinear MPC algorithm.

Time-Optimal Path Following for Robots With Convex–Concave Constraints Using Sequential Convex Programming

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time. In the case of a robotic manipulator with simplified constraints, a convex reformulation of this optimal control problem has been derived previously. However, many applications in robotics feature constraints such as velocity-dependent torque constraints or torque rate constraints that destroy the convexity. The present paper proposes an efficient sequential convex programming (SCP) approach to solve the corresponding nonconvex optimal control problems by writing the nonconvex constraints as a difference of convex (DC) functions, resulting in convex-concave constraints. We consider seven practical applications that fit into the proposed framework even when mutually combined, illustrating the flexibility and practicality of the proposed framework. Furthermore, numerical simulations for some typical applications illustrate the fast convergence of the proposed method in only a few SCP iterations, confirming the efficiency of the proposed framework.

Optimal Path Following for Differentially Flat Robotic Systems Through a Geometric Problem Formulation

Path following deals with the problem of following a geometric path with no predefined timing information and constitutes an important step in solving the motion-planning problem. For differentially flat systems, it has been shown that the projection of the dynamics along the geometric path onto a linear single-input system leads to a small dimensional optimal control problem. Although the projection simplifies the problem to great extent, the resulting problem remains difficult to solve, in particular in the case of nonlinear system dynamics and time-optimal problems. This paper proposes a nonlinear change of variables, using a time transformation, to arrive at a fixed end-time optimal control problem. Numerical simulations on a robotic manipulator and a quadrotor reveal that the proposed problem formulation is solved efficiently without requiring an accurate initial guess.

Time-optimal path following for robots with trajectory jerk constraints using sequential convex programming

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time. In the case of a robotic manipulator a convex reformulation of this optimal control problem has been derived previously [1]. However, the bang-bang nature of the time-optimal trajectories results in near-infinite jerks in joint space and operational (Cartesian) space. For systems with un-modeled flexibilities, this usually results in excitation of the resonant frequencies, hence in unwanted vibrations and acceleration peaks, contributing to a tracking error. These vibrations can be reduced by imposing jerk constraints on the trajectory [2]. However, these jerk constraints destroy the convexity of the time-optimal control problem. The present paper proposes an efficient sequential convex programming (SCP) approach to solve the corresponding non-convex optimal control problem by writing the non-convex jerk constraints as a difference of convex (DC) functions. We illustrate the developed approach by means of experiments with a seven d.o.f. robot. Furthermore, numerical simulations illustrate the fast convergence of the proposed method in only a few SCP iterations, confirming the efficiency and practicality of the proposed framework.

Iterative learning control for optimal path following problems

In optimal path following problems the motion along a given geometric path is optimized according to a desired objective while accounting for the system dynamics and system constraints. In the case of time-optimal path following, for example, the system input to move along the geometric path in minimal time is computed. In practice however, due to model-plant mismatch, (i) the geometric path is not followed exactly, and (ii) the optimized trajectory might be suboptimal, or even infeasible for the true plant. Assuming that the system performs the task repeatedly, this paper proposes an iterative learning control approach to improve the path following performance. The proposed learning algorithm is experimentally validated for a time-optimal path following problem on an XY-table. The results show that the developed ILC approach improves both the execution time and the accuracy significantly.

Convex time-optimal robot path following with Cartesian acceleration and inertial force and torque constraints:

In time-optimal robot path following, a predetermined geometric trajectory is followed exactly in a time-optimal way considering system constraints, for example, actuator constraints. For a simplified robotic manipulator, this optimization problem can be reformulated into a convex optimization problem when only considering some system constraints. In this article, the convex approach is extended to account for Cartesian acceleration constraints and in turn account for inertial forces and torques acting on a load held by the robot. The focus of this article is on the reformulation of these Cartesian acceleration and inertial forces and torques to preserve the convexity of the optimization problem. We present a series of applications that result in solving a convex optimization problem, illustrating the practicality of the proposed reformulations.

Real-time motion planning in the presence of moving obstacles

Safe operation of autonomous systems demands a collision-free motion trajectory at every time instant. This paper presents a method to calculate time-optimal motion trajectories for autonomous systems moving through an environment with both stationary and moving obstacles. To transform this motion planning problem into a small dimensional optimization problem, suitable for real-time optimization, the approach (i) uses a spline parameterization of the motion trajectory; and (ii) exploits spline properties to reduce the number of constraints. Solving this optimization problem with a receding horizon allows dealing with modeling errors and variations in the environment. In addition to extensive numerical simulations, the method is experimentally validated on a KUKA youBot. The average solving time of the optimization problem in the experiments is 0.05s, which is sufficiently fast for correcting deviations from the initial trajectory.

Optimal motion planning for differentially flat systems with guaranteed constraint satisfaction

This research deals with the computation of optimal trajectories considering state and input constraints for linear and nonlinear systems that admit a polynomial representation through differential flatness. Based on a polynomial spline parameterization of the flat output an optimization problem in terms of the B-spline coefficients is derived that guarantees constraint satisfaction over the entire time horizon whereas classical approaches in the literature only impose the constraints on a finite time grid. As the proposed constraints are only sufficient conditions, a novel method is presented that effectively reduces their conservatism. Two numerical examples, a linear benchmark tracking problem and an optimal quadrotor maneuver, illustrate the efficiency and practicality of the presented method.

Time-optimal path following for robots with object collision avoidance using lagrangian duality

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time while respecting system constraints. This paper focusses on time-optimal path following problems in robotics where collision must be avoided with other robots or moving obstacles. The developed method is based on the convex reformulation of the time-optimal path following problem with simplified dynamics presented in [1]. The robot and the obstacles are modelled as unions of convex polyhedra and the collision avoidance constraints are derived using Lagrangian duality. These constraints render the optimization problem non-convex. However, numerical simulations show that the resulting non-convex optimization problem can still be solved efficiently using a non-linear solver, due to the time-optimal path following formulation [1] and the proposed formulation of the collision avoidance constraints.

Time-optimal path planning for flat systems with application to a wheeled mobile robot

The time-optimal path planning problem aims at bringing a system from an initial to terminal state in minimal time while obeying both geometric and dynamic constraints. Path planning problems are often decoupled into a high-level path planning stage where a feasible geometric path is determined and a low level stage where system dynamics are taken into account. The paper combines the geometric and dynamic approach into a single optimization problem for so-called differentially flat systems. The geometric path is represented as a convex combination of two or more feasible paths. Relying on differential flatness, the dynamics of the system are projected onto the path which leads to a single input system. The resulting optimization problem is transformed into a fixed end-time optimal control problem that can be initialized easily. An application to a wheeled mobile robot, a challenging non-linear system, will illustrate the proposed approach throughout the paper.