Motion planning with time-varying polyhedral obstacles based on graph search and mathematical programming

SUMMARYWe propose a novel formal approach to robust motion planning (MP) in dynamic environments based on reachability analysis. While traditional MP methods usually fail to provide formal robust safety and performance guarantees, our approach provably ensures safe task achievement in time-varying and adversarial environments under parametric uncertainty. We leverage recent results on Hamilton–Jacobi (HJ) reachability and differential games in order to compute offline guaranteed motion plans that are compatible with the sampled-data (SD) paradigm. Also, we synthesize online provably robust safety-preserving and target-reaching feedback controls. Unlike earlier applications of reachability analysis to MP, our methodology handles arbitrary time-varying constraints, adversarial agents such as pursuing obstacles or evading targets, and takes into account the robot’s configuration. Furthermore, we use HJ projections in order to reduce significantly the computational burden without trading off safety guarantees. The validity of this approach is demonstrated through the case study of a robot arm subject to measurement errors, which is tasked with safely reaching a goal in a known time-varying workspace while avoiding capture by an unpredictable pursuer. Finally, the performance of the approach and research perspectives are discussed.

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Motion Planning Algorithm for Heterogeneous Combinatorial Robots in Time-Varying Environment

2007 IEEE International Conference on Automation and Logistics ◽

10.1109/ical.2007.4339094 ◽

2007 ◽

Author(s):

Hong-Fa Ho ◽

Wen-Xiong Liao

Keyword(s):

Motion Planning ◽

Time Varying ◽

Planning Algorithm ◽

Time Varying Environment ◽

Varying Environment

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Motion Planning of a Group of Agents Using the Homotopy Approach

Volume 9: Mechanical Systems and Control, Parts A, B, and C ◽

10.1115/imece2007-42677 ◽

2007 ◽

Author(s):

Mayank Lal ◽

Suhada Jayasuriya ◽

Swaminathan Sethuraman

Keyword(s):

Motion Planning ◽

Mobile Agents ◽

Single Agent ◽

Initial Configuration ◽

Potential Fields ◽

Polynomial Space ◽

Time Varying ◽

Multiple Roots ◽

Final Configuration ◽

Discriminant Variety

In this paper motion planning of a group of agents is done to move the group from an initial configuration to a final configuration through obstacles in 2-D. Also we introduce a new homotopy approach which uses potential fields to find paths in polynomial space. We use the homotopy approach for changing the group shape of the mobile agents and at the same time treat the group as a single agent by finding a bounding disc for it to plan the motion of the group through obstacles. A time varying polynomial is constructed, the roots of which represent the current positions of the mobile agents in a frame attached to the bounding disc. The real and imaginary parts of the roots of this polynomial represent the x and y coordinates of the mobile agents in this frame. This polynomial is constructed such that it avoids the discriminant variety or the set of polynomials having multiple roots. This is equivalent to saying that the mobile agents do not collide with each other at all times. The bounding disc is then used to plan the motion of the agents through obstacles such that the group avoids the obstacles at all times.

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