An official website of the United States government
Nonlinear optimal control problems are challenging to solve efficiently due to non-convexity. This paper introduces a trajectory optimization approach that achieves real-time performance by combining machine learning to predict optimal trajectories with refinement by quadratic optimization. First, a library of optimal trajectories is calculated offline and used to train a neural network. Online, the neural network predicts a trajectory for a novel initial state and cost function, and this prediction is further optimized by a sparse quadratic programming solver. We apply this approach to a fly-to-target movement problem for an indoor quadrotor. Experiments demonstrate that the technique calculates near-optimal trajectories in a few milliseconds, and generates agile movement that can be tracked more accurately than existing methods.
more »
« less
MPCGPU: Real-Time Nonlinear Model Predictive Control through Preconditioned Conjugate Gradient on the GPU
Nonlinear Model Predictive Control (NMPC) is a state-of-the-art approach for locomotion and manipulation which leverages trajectory optimization at each control step. While the performance of this approach is computationally bounded, implementations of direct trajectory optimization that use iterative methods to solve the underlying moderately-large and sparse linear systems, are a natural fit for parallel hardware acceleration. In this work, we introduce MPCGPU, a GPU-accelerated, real-time NMPC solver that leverages an accelerated preconditioned conjugate gradient (PCG) linear system solver at its core. We show that MPCGPU increases the scalability and real-time performance of NMPC, solving larger problems, at faster rates. In particular, for tracking tasks using the Kuka IIWA manipulator, MPCGPU is able to scale to kilohertz control rates with trajectories as long as 512 knot points. This is driven by a custom PCG solver which outperforms state-of-the-art, CPU-based, linear system solvers by at least 10x for a majority of solves and 3.6x on average.
more »
« less
- Award ID(s):
- 2246022
- PAR ID:
- 10532063
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 979-8-3503-8457-4
- Page Range / eLocation ID:
- 9787 to 9794
- Format(s):
- Medium: X
- Location:
- Yokohama, Japan
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Path planning is a critical task for autonomous driving, aiming to generate smooth, collision-free, and feasible paths based on input perception and localization information. The planning task is both highly time-sensitive and computationally intensive, posing significant challenges to resource-constrained autonomous driving hardware. In this article, we propose an end-to-end framework for accelerating path planning on FPGA platforms. This framework focuses on accelerating quadratic programming (QP) solving, which is the core of optimization-based path planning and has the most computationally-intensive workloads. Our method leverages a hardware-friendly alternating direction method of multipliers (ADMM) to solve QP problems while employing a highly parallelizable preconditioned conjugate gradient (PCG) method for solving the associated linear systems. We analyze the sparse patterns of matrix operations in QP and design customized storage schemes along with efficient sparse matrix multiplication and sparse matrix-vector multiplication units. Our customized design significantly reduces resource consumption for data storage and computation while dramatically speeding up matrix operations. Additionally, we propose a multi-level dataflow optimization strategy. Within individual operators, we achieve acceleration through parallelization and pipelining. For different operators in an algorithm, we analyze inter-operator data dependencies to enable fine-grained pipelining. At the system level, we map different steps of the planning process to the CPU and FPGA and pipeline these steps to enhance end-to-end throughput. We implement and validate our design on the AMD ZCU102 platform. Our implementation achieves state-of-the-art performance in both latency and energy efficiency compared with existing works, including an average 1.48× speedup over the best FPGA-based design, a 2.89× speedup compared with the state-of-the-art QP solver on an Intel i7-11800H CPU, a 5.62× speedup over an ARM Cortex-A57 embedded CPU, and a 1.56× speedup over state-of-the-art GPU-based work. Furthermore, our design delivers a 2.05× improvement in throughput compared with the state-of-the-art FPGA-based design.more » « less
-
This paper addresses the problem of learning the optimal control policy for a nonlinear stochastic dynam- ical. This problem is subject to the ‘curse of dimension- ality’ associated with the dynamic programming method. This paper proposes a novel decoupled data-based con- trol (D2C) algorithm that addresses this problem using a decoupled, ‘open-loop - closed-loop’, approach. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system. Then, closed-loop control is developed around this open-loop trajectory by linearization of the dynamics about this nominal trajectory. By virtue of linearization, a linear quadratic regulator based algorithm can be used for this closed-loop control. We show that the performance of D2C algorithm is approximately optimal. Moreover, simulation performance suggests a significant reduction in training time compared to other state of the art algorithms.more » « less
-
Abstract Convergence analysis of accelerated first-order methods for convex optimization problems are developed from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient (NAG) flow, is derived from the connection between acceleration mechanism andA-stability of ODE solvers, and the exponential decay of a tailored Lyapunov function along with the solution trajectory is proved. Numerical discretizations of NAG flow are then considered and convergence rates are established via a discrete Lyapunov function. The proposed differential equation solver approach can not only cover existing accelerated methods, such as FISTA, Güler’s proximal algorithm and Nesterov’s accelerated gradient method, but also produce new algorithms for composite convex optimization that possess accelerated convergence rates. Both the convex and the strongly convex cases are handled in a unified way in our approach.more » « less
-
The transition from batch to continuous processes in the pharmaceutical industry has been driven by the potential improvement in process controllability, product quality homogeneity, and reduction of material inventory. A quality-by-control (QbC) approach has been implemented in a variety of pharmaceutical product manufacturing modalities to increase product quality through a three-level hierarchical control structure. In the implementation of the QbC approach it is common practice to simplify control algorithms by utilizing linearized models with constant model parameters. Nonlinear model predictive control (NMPC) can effectively deliver control functionality for highly sensitive variations and nonlinear multiple-input-multiple-output (MIMO) systems, which is essential for the highly regulated pharmaceutical manufacturing industry. This work focuses on developing and implementing NMPC in continuous manufacturing of solid dosage forms. To mitigate control degradation caused by plant-model mismatch, careful monitoring and continuous improvement strategies are studied. When moving horizon estimation (MHE) is integrated with NMPC, historical data in the past time window together with real-time data from the sensor network enable state estimation and accurate tracking of the highly sensitive model parameters. The adaptive model used in the NMPC strategy can compensate for process uncertainties, further reducing plant-model mismatch effects. The nonlinear mechanistic model used in both MHE and NMPC can predict the essential but complex powder properties and provide physical interpretation of abnormal events. The adaptive NMPC implementation and its real-time control performance analysis and practical applicability are demonstrated through a series of illustrative examples that highlight the effectiveness of the proposed approach for different scenarios of plant-model mismatch, while also incorporating glidant effects.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICRA57147.2024.10611212
