Real-Time Quad-Rotor Path Planning Using Convex Optimization and Compound State-Triggered Constraints

Abstract

The contribution of this paper is the application of compound state-triggered constraints (STCs) to real-time quadrotor path planning. Originally developed for rocket landing applications, STCs are made up of a trigger condition and a constraint condition that are arranged such that satisfaction of the former implies satisfaction of the latter. Compound STCs go a step further by allowing multiple trigger and constraint conditions to be combined via Boolean "and" or "or" operations. The logical implications embodied by STCs can be formulated using continuous variables, and thus enable the incorporation of discrete decision making into a continuous optimization framework. In this paper, compound STCs are used to solve quad-rotor path planning problems that would typically require the use of computationally expensive mixedinteger programming techniques. Two scenarios are considered:(1) a quad-rotor flying through a hoop, and (2) a pair of quadrotors carrying a beam-like payload through an obstacle course. Successive convexification is used to solve the resulting nonconvex optimization problem. Monte-Carlo simulation results show that our approach can reliably generate trajectories at rates upwards of 3 and 1.5 Hz for the first and second scenarios, respectively.

Fast Homotopy for Spacecraft Rendezvous Trajectory Optimization with Discrete Logic

“…RASHS [22] CSC [23,24] STCs Slack variable [25][26][27] Multiplicative coefficient [28,29] Compound logic [30,31] Proposed method that it uses numerical optimization to solve a discretized version of the optimal control problem. This generally makes it easier to handle constraints, which are nontrivial to include in an indirect approach.…”

“…Two equivalent forms of STCs have been proposed, based on a slack variable [25] and based on a multiplicative coefficient that is motivated by the linear complementarity problem [28]. STCs have also been extended to handle quite general logical combinations of and and or gates [30,31].…”

“…Equation (31) together with (30) enforce 0 ≤ Δ𝑡 𝑖𝑘 ≤ 0 when the predicate (29) is true, which is equivalent to (12g). When the chaser is outside of the plume impingement sphere, the forward-facing thrusters are free to fire.…”

Fast Trajectory Optimization via Successive Convexification for Spacecraft Rendezvous with Integer Constraints

“…Even though Problem 1 is finite dimensional after discretization, it is still a non-convex optimization problem due to the presence of the state-triggered constraints (10g)-(10i). This type of constraint has recently been formalized for the method of successive convexification [13,14,[22][23][24] and is generally written as:…”

“…Since our intent is to demonstrate the capability, we do not explore these cases but only stress that their inclusion is entirely possible while maintaining computational tractability. Some other applications of state-triggered constraints can be found in [13,14,[22][23][24].…”