374 research outputs found
RDA: An Accelerated Collision Free Motion Planner for Autonomous Navigation in Cluttered Environments
Autonomous motion planning is challenging in multi-obstacle environments due
to nonconvex collision avoidance constraints. Directly applying numerical
solvers to these nonconvex formulations fails to exploit the constraint
structures, resulting in excessive computation time. In this paper, we present
an accelerated collision-free motion planner, namely regularized dual
alternating direction method of multipliers (RDADMM or RDA for short), for the
model predictive control (MPC) based motion planning problem. The proposed RDA
addresses nonconvex motion planning via solving a smooth biconvex reformulation
via duality and allows the collision avoidance constraints to be computed in
parallel for each obstacle to reduce computation time significantly. We
validate the performance of the RDA planner through path-tracking experiments
with car-like robots in both simulation and real-world settings. Experimental
results show that the proposed method generates smooth collision-free
trajectories with less computation time compared with other benchmarks and
performs robustly in cluttered environments. The source code is available at
https://github.com/hanruihua/RDA_planner.Comment: Published in: IEEE Robotics and Automation Letters ( Volume: 8,
Issue: 3, March 2023) (https://ieeexplore.ieee.org/document/10036019
A recursively feasible and convergent Sequential Convex Programming procedure to solve non-convex problems with linear equality constraints
A computationally efficient method to solve non-convex programming problems
with linear equality constraints is presented. The proposed method is based on
a recursively feasible and descending sequential convex programming procedure
proven to converge to a locally optimal solution. Assuming that the first
convex problem in the sequence is feasible, these properties are obtained by
convexifying the non-convex cost and inequality constraints with inner-convex
approximations. Additionally, a computationally efficient method is introduced
to obtain inner-convex approximations based on Taylor series expansions. These
Taylor-based inner-convex approximations provide the overall algorithm with a
quadratic rate of convergence. The proposed method is capable of solving
problems of practical interest in real-time. This is illustrated with a
numerical simulation of an aerial vehicle trajectory optimization problem on
commercial-of-the-shelf embedded computers
Fast Second-order Cone Programming for Safe Mission Planning
This paper considers the problem of safe mission planning of dynamic systems
operating under uncertain environments. Much of the prior work on achieving
robust and safe control requires solving second-order cone programs (SOCP).
Unfortunately, existing general purpose SOCP methods are often infeasible for
real-time robotic tasks due to high memory and computational requirements
imposed by existing general optimization methods. The key contribution of this
paper is a fast and memory-efficient algorithm for SOCP that would enable
robust and safe mission planning on-board robots in real-time. Our algorithm
does not have any external dependency, can efficiently utilize warm start
provided in safe planning settings, and in fact leads to significant speed up
over standard optimization packages (like SDPT3) for even standard SOCP
problems. For example, for a standard quadrotor problem, our method leads to
speedup of 1000x over SDPT3 without any deterioration in the solution quality.
Our method is based on two insights: a) SOCPs can be interpreted as
optimizing a function over a polytope with infinite sides, b) a linear function
can be efficiently optimized over this polytope. We combine the above
observations with a novel utilization of Wolfe's algorithm to obtain an
efficient optimization method that can be easily implemented on small embedded
devices. In addition to the above mentioned algorithm, we also design a
two-level sensing method based on Gaussian Process for complex obstacles with
non-linear boundaries such as a cylinder
Unsupervised learning for long-term autonomy
This thesis investigates methods to enable a robot to build and maintain an environment model in an automatic manner. Such capabilities are especially important in long-term autonomy, where robots operate for extended periods of time without human intervention. In such scenarios we can no longer assume that the environment and the models will remain static. Rather changes are expected and the robot needs to adapt to the new, unseen, circumstances automatically. The approach described in this thesis is based on clustering the robotโs sensing information. This provides a compact representation of the data which can be updated as more information becomes available. The work builds on affinity propagation (Frey and Dueck, 2007), a recent clustering method which obtains high quality clusters while only requiring similarities between pairs of points, and importantly, selecting the number of clusters automatically. This is essential for real autonomy as we typically do not know โa prioriโ how many clusters best represent the data. The contributions of this thesis a three fold. First a self-supervised method capable of learning a visual appearance model in long-term autonomy settings is presented. Secondly, affinity propagation is extended to handle multiple sensor modalities, often occurring in robotics, in a principle way. Third, a method for joint clustering and outlier selection is proposed which selects a user defined number of outlier while clustering the data. This is solved using an extension of affinity propagation as well as a Lagrangian duality approach which provides guarantees on the optimality of the solution
Edge Accelerated Robot Navigation with Hierarchical Motion Planning
Low-cost autonomous robots suffer from limited onboard computing power,
resulting in excessive computation time when navigating in cluttered
environments. This paper presents Edge Accelerated Robot Navigation, or EARN
for short, to achieve real-time collision avoidance by adopting hierarchical
motion planning (HMP). In contrast to existing local or edge motion planning
solutions that ignore the interdependency between low-level motion planning and
high-level resource allocation, EARN adopts model predictive switching (MPS)
that maximizes the expected switching gain w.r.t. robot states and actions
under computation and communication resource constraints. As such, each robot
can dynamically switch between a point-mass motion planner executed locally to
guarantee safety (e.g., path-following) and a full-shape motion planner
executed non-locally to guarantee efficiency (e.g., overtaking). The crux to
EARN is a two-time scale integrated decision-planning algorithm based on
bilevel mixed-integer optimization, and a fast conditional collision avoidance
algorithm based on penalty dual decomposition. We validate the performance of
EARN in indoor simulation, outdoor simulation, and real-world environments.
Experiments show that EARN achieves significantly smaller navigation time and
collision ratios than state-of-the-art navigation approaches.Comment: 12 pages, 14 figures, 1 table, submitted to IEEE for possible
publicatio
ํ์ต ๊ธฐ๋ฐ ์์จ์์คํ ์ ๋ฆฌ์คํฌ๋ฅผ ๊ณ ๋ คํ๋ ๋ถํฌ์ ๊ฐ์ธ ์ต์ ํ
ํ์๋
ผ๋ฌธ (์์ฌ) -- ์์ธ๋ํ๊ต ๋ํ์ : ๊ณต๊ณผ๋ํ ์ ๊ธฐยท์ ๋ณด๊ณตํ๋ถ, 2020. 8. ์์ธ์.In this thesis, a risk-aware motion control scheme is considered for autonomous systems to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model predictive control (MPC) method for motion planning and decision-making that systematically adjusts the safety and conservativeness in an environment with randomly moving obstacles. The key component is the Conditional Value-at-Risk (CVaR), employed to limit the safety risk in the MPC problem. Having the empirical distribution obtained using a limited amount of sample data, Sample Average Approximation (SAA) is applied to compute the safety risk. Furthermore, we propose a method, which limits the risk of unsafety even when the true distribution of the obstacles movements deviates, within an ambiguity set, from the empirical one. By choosing the ambiguity set as a statistical ball with its radius measured by the Wasserstein metric, we achieve a probabilistic guarantee of the out-of-sample risk, evaluated using new sample data generated independently of the training data. A set of reformulations are applied on both SAA-based MPC (SAA-MPC) and Wasserstein Distributionally Robust MPC (DR-MPC) to make them tractable.
In addition, we combine the DR-MPC method with Gaussian Process (GP) to predict the future motion of the obstacles from past observations of the environment.
The performance of the proposed methods is demonstrated and analyzed through simulation studies using a nonlinear vehicle model and a linearized quadrotor model.๋ณธ ์ฐ๊ตฌ์์ ์์จ ์์คํ
์ด ์๋ ค์ง์ง ์์ ํ๋ฅ ๋ถํฌ๋ก ๋๋คํ๊ฒ ์์ง์ด๋ ์ฅ์ ๋ฌผ์ ํผํ๊ธฐ ์ํ ์ํ ์ธ์์ ๊ณ ๋ คํ๋ ๋ชจ์
์ ์ด ๊ธฐ๋ฒ์ ๊ฐ๋ฐํ๋ค. ๋ฐ๋ผ์ ๋ณธ ๋
ผ๋ฌธ์์ ์์ ์ฑ๊ณผ ๋ณด์์ฑ์ ์ฒด๊ณ์ ์ผ๋ก ์กฐ์ ํ๋ ์๋ก์ด Model Predictive Control (MPC) ๋ฐฉ๋ฒ์ ์ ์ํ๋ค. ๋ณธ ๋ฐฉ๋ฒ์ ํต์ฌ ์์๋ MPC ๋ฌธ์ ์ ์์ ์ฑ ๋ฆฌ์คํฌ๋ฅผ ์ ํํ๋ Conditional Value-at-Risk (CVaR)๋ผ๋ ๋ฆฌ์คํฌ ์ฒ๋์ด๋ค. ์์ ์ฑ ๋ฆฌ์คํฌ๋ฅผ ๊ณ์ฐํ๊ธฐ ์ํด ์ ํ๋ ์์ ํ๋ณธ ๋ฐ์ดํฐ๋ฅผ ์ด์ฉํ์ฌ ์ป์ด์ง ๊ฒฝํ์ ๋ถํฌ๋ฅผ ์ฌ์ฉํ๋ Sample Average Approximation (SAA)์ ์ ์ฉํ๋ค.
๋ํ, ๊ฒฝํ์ ๋ถํฌ๋ก๋ถํฐ ์ค์ ๋ถํฌ๊ฐ Ambiguity Set๋ผ๋ ์งํฉ ๋ด์์ ๋ฒ์ด๋๋ ๋ฆฌ์คํฌ๋ฅผ ์ ํํ๋ ๋ฐฉ๋ฒ์ ์ ์ํ๋ค.
Ambiguity Set๋ฅผ Wasserstein ๊ฑฐ๋ฆฌ๋ก ์ธก์ ๋ ๋ฐ์ง๋ฆ์ ๊ฐ์ง ํต๊ณ์ ๊ณต์ผ๋ก ์ ํํจ์ผ๋ก์จ ํ๋ จ ๋ฐ์ดํฐ์ ๋
๋ฆฝ์ ์ผ๋ก ์์ฑ๋ ์๋ก์ด ์ํ ๋ฐ์ดํฐ๋ฅผ ์ฌ์ฉํ์ฌ ํ๊ฐํ out-of-sample risk์ ๋ํ ํ๋ฅ ์ ๋ณด์ฅ์ ๋ฌ์ฑํ๋ค.
๋ณธ ๋
ผ๋ฌธ์์ SAA๊ธฐ๋ฐ MPC (SAA-MPC)์ Wasserstein Distributionally Robust MPC (DR-MPC)๋ฅผ ์ฌ๋ฌ ๊ณผ์ ์ ํตํ์ฌ ๋ค๋ฃจ๊ธฐ ์ฌ์ด ํ๋ก๊ทธ๋จ์ผ๋ก ์ฌํธ์ฑํ๋ค.
๋ํ, ํ๊ฒฝ์ ๊ณผ๊ฑฐ ๊ด์ธก์ผ๋ก๋ถํฐ ์ฅ์ ๋ฌผ์ ๋ฏธ๋ ์์ง์์ ์์ธกํ๊ธฐ ์ํด Distributionally Robust MPC ๋ฐฉ๋ฒ์ Gaussian Process (GP)์ ๊ฒฐํฉํ๋ค. ๋ณธ ์ฐ๊ตฌ์์ ๊ฐ๋ฐ๋๋ ๊ธฐ๋ฒ๋ค์ ์ฑ๋ฅ์ ๋น์ ํ ์๋์ฐจ ๋ชจ๋ธ๊ณผ ์ ํํ๋ ์ฟผ๋๋กํฐ ๋ชจ๋ธ์ ์ด์ฉํ ์๋ฎฌ๋ ์ด์
์ฐ๊ตฌ๋ฅผ ํตํ์ฌ ๋ถ์ํ๋ค.1 BACKGROUND AND OBJECTIVES 1
1.1 Motivation and Objectives 1
1.2 Research Contributions 2
1.3 Thesis Organization 3
2 RISK-AWARE MOTION PLANNING AND CONTROL USING CVAR-CONSTRAINED OPTIMIZATION 5
2.1 Introduction 5
2.2 System and Obstacle Models 8
2.3 CVaR-constrained Motion Planning and Control 10
2.3.1 Reference Trajectory Planning 10
2.3.2 Safety Risk 11
2.3.3 Risk-Constrained Model Predictive Control 13
2.3.4 Linearly Constrained Mixed Integer Convex Program 18
2.4 Numerical Experiments 20
2.4.1 Effect of Confidence Level 21
2.4.2 Effect of Sample Size 23
2.5 Conclusions 24
3 WASSERSTEIN DISTRIBUTIONALLY ROBUST MPC 28
3.1 Introduction 28
3.2 System and Obstacle Models 31
3.3 Wasserstein Distributionally Robust MPC 33
3.3.1 Distance to the Safe Region 36
3.3.2 Reformulation of Distributionally Robust Risk Constraint 38
3.3.3 Reformulation of the Wasserstein DR-MPC Problem 43
3.4 Out-of-Sample Performance Guarantee 45
3.5 Numerical Experiments 47
3.5.1 Nonlinear Car-Like Vehicle Model 48
3.5.2 Linearized Quadrotor Model 53
3.6 Conclusions 57
4 LEARNING-BASED DISTRIBUTIONALLY ROBUST MPC 58
4.1 Introduction 58
4.2 Learning the Movement of Obstacles Using Gaussian Processes 60
4.2.1 Obstacle Model 60
4.2.2 Gaussian Process Regression 61
4.2.3 Prediction of the Obstacle's Motion 63
4.3 Gaussian Process based Wasserstein DR-MPC 65
4.4 Numerical Experiments 70
4.5 Conclusions 74
5 CONCLUSIONS AND FUTURE WORK 75
Abstract (In Korean) 87Maste
Communication-based Decentralized Cooperative Object Transportation Using Nonlinear Model Predictive Control
This paper addresses the problem of cooperative transportation of an object
rigidly grasped by N robotic agents. We propose a Nonlinear Model Predictive
Control (NMPC) scheme that guarantees the navigation of the object to a desired
pose in a bounded workspace with obstacles, while complying with certain input
saturations of the agents. The control scheme is based on inter-agent
communication and is decentralized in the sense that each agent calculates its
own control signal. Moreover, the proposed methodology ensures that the agents
do not collide with each other or with the workspace obstacles as well as that
they do not pass through singular configurations. The feasibility and
convergence analysis of the NMPC are explicitly provided. Finally, simulation
results illustrate the validity and efficiency of the proposed method.Comment: European Control Conference 2018. arXiv admin note: text overlap with
arXiv:1705.0142
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