SearcharxivSearch

arXiv subjects

Lander Vanroye

Publications and source records attributed to Lander Vanroye.

5 recordsLinked to original sources

Accelerated Multi-Modal Motion Planning Using Context-Conditioned Diffusion Models

Classical methods in robot motion planning, such as sampling-based and optimization-based methods, often struggle with scalability towards higher-dimensional state spaces and complex environments. Diffusion models, known for their capability to learn complex, high-dimensional and multi-modal data distributions, provide a promising alternative when applied to motion planning problems and have already shown interesting results. However, most of the current approaches train their model for a single environment, limiting their generalization to environments not seen during training. The techniques that do train a model for multiple environments rely on a specific camera to provide the model with the necessary environmental information and therefore always require that sensor. To effectively adapt to diverse scenarios without the need for retraining, this research proposes Context-Aware Motion Planning Diffusion (CAMPD). CAMPD leverages a classifier-free denoising probabilistic diffusion model, conditioned on sensor-agnostic contextual information. An attention mechanism, integrated in the well-known U-Net architecture, conditions the model on an arbitrary number of contextual parameters. CAMPD is evaluated on a 7-DoF robot manipulator and benchmarked against state-of-the-art approaches on real-world tasks, showing its ability to generalize to unseen environments and generate high-quality, multi-modal trajectories, at a fraction of the time required by existing methods.

cs.RO

ASAP-MPC: An Asynchronous Update Scheme for Online Motion Planning with Nonlinear Model Predictive Control

This paper presents a Nonlinear Model Predictive Control (NMPC) scheme targeted at motion planning for mechatronic motion systems, such as drones and mobile platforms. NMPC-based motion planning typically requires low computation times to be able to provide control inputs at the required rate for system stability, disturbance rejection, and overall performance. Although there exist various ways in literature to reduce the solution times in NMPC, such times may not be low enough to allow real-time implementations. This paper presents ASAP-MPC, an approach to handle varying, sometimes restrictively large, solution times with an asynchronous update scheme, always allowing for full convergence and real-time execution. The NMPC algorithm is combined with a linear state feedback controller tracking the optimised trajectories for improved robustness against possible disturbances and plant-model mismatch. ASAP-MPC seamlessly merges trajectories, resulting from subsequent NMPC solutions, providing a smooth and continuous overall trajectory for the motion system. This frameworks applicability to embedded applications is shown on two different experiment setups where a state-of-the-art method fails: a quadcopter flying through a cluttered environment in hardware-in-the-loop simulation and a scale model truck-trailer manoeuvring in a structured lab environment.

cs.RO

FATROP : A Fast Constrained Optimal Control Problem Solver for Robot Trajectory Optimization and Control

Trajectory optimization is a powerful tool for robot motion planning and control. State-of-the-art general-purpose nonlinear programming solvers are versatile, handle constraints effectively and provide a high numerical robustness, but they are slow because they do not fully exploit the optimal control problem structure at hand. Existing structure-exploiting solvers are fast, but they often lack techniques to deal with nonlinearity or rely on penalty methods to enforce (equality or inequality) path constraints. This work presents Fatrop: a trajectory optimization solver that is fast and benefits from the salient features of general-purpose nonlinear optimization solvers. The speed-up is mainly achieved through the integration of a specialized linear solver, based on a Riccati recursion that is generalized to also support stagewise equality constraints. To demonstrate the algorithm's potential, it is benchmarked on a set of robot problems that are challenging from a numerical perspective, including problems with a minimum-time objective and no-collision constraints. The solver is shown to solve problems for trajectory generation of a quadrotor, a robot manipulator and a truck-trailer problem in a few tens of milliseconds. The algorithm's C++-code implementation accompanies this work as open source software, released under the GNU Lesser General Public License (LGPL). This software framework may encourage and enable the robotics community to use trajectory optimization in more challenging applications.

math.OC

A Generalization of the Riccati Recursion for Equality-Constrained Linear Quadratic Optimal Control

This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal feedback control policies. Unlike other tailored approaches for this problem class, the proposed method does not require restrictive regularity conditions on the problem. This allows its use in nonlinear optimal control problem solvers that use exact Lagrangian Hessian information. We demonstrate that our approach can be implemented in a highly efficient algorithm that scales linearly with the horizon length. Numerical tests show a significant speed-up of up to two orders of magnitude with respect to state-of-the-art general-purpose sparse linear solvers. Based on the proposed approach, faster nonlinear optimal control problem solvers can be developed that are suitable for more complex applications or for implementations on low-cost or low-power computational platforms. The implementation of the proposed algorithm is made available as open-source software.

math.OC

Reversible random number generation for adjoint Monte Carlo simulation of the heat equation

In PDE-constrained optimization, one aims to find design parameters that minimize some objective, subject to the satisfaction of a partial differential equation. A major challenges is computing gradients of the objective to the design parameters, as applying the chain rule requires computing the Jacobian of the design parameters to the PDE's state. The adjoint method avoids this Jacobian by computing partial derivatives of a Lagrangian. Evaluating these derivatives requires the solution of a second PDE with the adjoint differential operator to the constraint, resulting in a backwards-in-time simulation. Particle-based Monte Carlo solvers are often used to compute the solution to high-dimensional PDEs. However, such solvers have the drawback of introducing noise to the computed results, thus requiring stochastic optimization methods. To guarantee convergence in this setting, both the constraint and adjoint Monte Carlo simulations should simulate the same particle trajectories. For large simulations, storing full paths from the constraint equation for re-use in the adjoint equation becomes infeasible due to memory limitations. In this paper, we provide a reversible extension to the family of permuted congruential pseudorandom number generators (PCG). We then use such a generator to recompute these time-reversed paths for the heat equation, avoiding these memory issues.

math.NA