MINVO Basis: Finding Simplexes with Minimum Volume Enclosing Polynomial Curves

Tordesillas, Jesus; How, Jonathan P.

doi:10.48550/arxiv.2010.10726

Cited by 5 publications

(7 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the obstacle avoidance of dynamic obstacles, and similar to our previous work [28], we first create a polyhedral outer representation of both the trajectory of the agent and of the obstacle (see Fig. 5): For the agent, we make use of the MINVO basis [1] (a polynomial basis that finds the simplex with minimum volume enclosing a polynomial curve) to obtain the set of control points Q MV j whose convex hull encloses each segment j of the agent. Similarly, for each obstacle i, we first compute the MINVO control points of the segment j (using the predicted mean (p i ) w (t)), and then we inflate it with norminv (1 − δ, δ) • σ i (t end j ), half of the sides the AABB (axis-aligned bounding box) of the obstacle i and half of the sides of the AABB of the agent.…”

Section: B Collision Avoidance and Dynamic Limits Constraintsmentioning

confidence: 99%

“…In other words, given a spatial trajectory in time, two degrees of freedom of the rotation are already determined by the acceleration at every point of the trajectory. This leaves only one extra degree of freedom (usually referred to as yaw 1 ).…”

Section: Introduction and Related Workmentioning

confidence: 99%

“…The authors are with the Aerospace Controls Laboratory, MIT, 77 Massachusetts Ave., Cambridge, MA, USA {jtorde, jhow}@mit.edu 1 The specific Euler convention for this yaw angle changes throughout the literature. The yaw convention rZYX (or, equivalently, sXYZ) is usually a common choice for UAVs.…”

Section: Introduction and Related Workmentioning

confidence: 99%

See 2 more Smart Citations

PANTHER: Perception-Aware Trajectory Planner in Dynamic Environments

Tordesillas,

How

2021

Preprint

Self Cite

View full text Add to dashboard Cite

This paper presents PANTHER, a real-time perception-aware (PA) trajectory planner in dynamic environments. PANTHER plans trajectories that avoid dynamic obstacles while also keeping them in the sensor field of view (FOV) and minimizing the blur to aid in object tracking. The rotation and translation of the UAV are jointly optimized, which allows PANTHER to fully exploit the differential flatness of multirotors. Real-time performance is achieved by implicitly imposing this constraint through the Hopf fibration. PANTHER is able to keep the obstacles inside the FOV 7.4 and 1.5 times more than non-PA approaches and PA approaches that decouple translation and yaw, respectively. The projected velocity (and hence the blur) is reduced by ≈30%. Our recently-derived MINVO basis [1] is used to impose low-conservative collision avoidance constraints in position and velocity space. Finally, extensive hardware experiments in unknown dynamic environments with all the computation running onboard are presented, with velocities of up to 5.8 m/s, and with relative velocities (with respect to the obstacles) of up to 6.3 m/s. The only sensors used are an IMU, a forwardfacing depth camera, and a downward-facing monocular camera.

show abstract

Section: B Collision Avoidance and Dynamic Limits Constraintsmentioning

confidence: 99%

Section: Introduction and Related Workmentioning

confidence: 99%

See 1 more Smart Citation

PANTHER: Perception-Aware Trajectory Planner in Dynamic Environments

Tordesillas,

How

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Many works [8,14,18] follow this underlying property and show successful applications in aerial swarms. However, this property indeed brings conservativeness, as analyzed by Tordesillas and How [19], preventing a trajectory from being aggressive near its physical limits. Besides, an n order B-Spline is naturally n − 1 order continuous [6].…”

Section: Related Work a Trajectory Parameterization For Aerial Robotsmentioning

confidence: 99%

Decentralized Spatial-Temporal Trajectory Planning for Multicopter Swarms

Zhou,

Wang,

Wen

et al. 2021

Preprint

View full text Add to dashboard Cite

Multicopter swarms with decentralized structure possess the nature of flexibility and robustness, while efficient spatial-temporal trajectory planning still remains a challenge. This report introduces decentralized spatial-temporal trajectory planning, which puts a well-formed trajectory representation named MINCO into multi-agent scenarios. Our method ensures high-quality local planning for each agent subject to any constraint from either the coordination of the swarm or safety requirements in cluttered environments. Then, the local trajectory generation is formulated as an unconstrained optimization problem that is efficiently solved in milliseconds. Moreover, a decentralized asynchronous mechanism is designed to trigger the local planning for each agent. A systematic solution is presented with detailed descriptions of careful engineering considerations. Extensive benchmarks and indoor/outdoor experiments validate its wide applicability and high quality. Our software will be released for the reference of the community.

show abstract

“…The other method is to add constraints on a set of control points, which are the vertices of the convex hull containing the segment, but it suffers from conservativeness. A recent work [24] proposes the MINVO basis, which has been shown to be less conservative than the widely used Bezier basis. We use the MINVO basis to construct a set of control points for our polynomial trajectory.…”

Section: Constraintsmentioning

confidence: 99%

DIRECT: A Differential Dynamic Programming Based Framework for Trajectory Generation

Cao¹,

Cao²,

Yuan³

et al. 2021

Preprint

View full text Add to dashboard Cite

This paper introduces a differential dynamic programming (DDP) based framework for polynomial trajectory generation for differentially flat systems. In particular, instead of using a linear equation with increasing size to represent multiple polynomial segments as in literature, we take a new perspective from state-space representation such that the linear equation reduces to a finite horizon control system with a fixed state dimension and the required continuity conditions for consecutive polynomials are automatically satisfied. Consequently, the constrained trajectory generation problem (both with and without time optimization) can be converted to a discrete-time finite-horizon optimal control problem with inequality constraints, which can be approached by a recently developed interior-point DDP (IPDDP) algorithm. Furthermore, for unconstrained trajectory generation with preallocated time, we show that this problem is indeed a linear-quadratic tracking (LQT) problem (DDP algorithm with exact one iteration). All these algorithms enjoy linear complexity with respect to the number of segments. Both numerical comparisons with stateof-the-art methods and physical experiments are presented to verify and validate the effectiveness of our theoretical findings. The implementation code will be open-sourced 1 .

show abstract

MINVO Basis: Finding Simplexes with Minimum Volume Enclosing Polynomial Curves

Cited by 5 publications

References 33 publications

PANTHER: Perception-Aware Trajectory Planner in Dynamic Environments

PANTHER: Perception-Aware Trajectory Planner in Dynamic Environments

Decentralized Spatial-Temporal Trajectory Planning for Multicopter Swarms

DIRECT: A Differential Dynamic Programming Based Framework for Trajectory Generation

Contact Info

Product

Resources

About