PRO-SPECT: Probabilistically Safe Scalable Planning for Energy-Aware Coordinated UAV-UGV Teams in Stochastic Environments

Roger Fowler; Cahit Ikbal Er; Benjamin Johnsenberg; Yasin Yazicioglu

cs.ROApr 2, 2026

PRO-SPECT: Probabilistically Safe Scalable Planning for Energy-Aware Coordinated UAV-UGV Teams in Stochastic Environments

Authors: Roger Fowler, Cahit Ikbal Er, Benjamin Johnsenberg, Yasin Yazicioglu

Organizations: Khoury Department of Computer Sciences, Northeastern University, Boston, MA · The Charles Stark Draper Laboratory, Inc., Cambridge, MA · Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA · Departments of Mechanical and Industrial Engineering and Electrical and Computer Engineering, Northeastern University, Boston, MA

Abstract

We consider energy-aware planning for an unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) team operating in a stochastic environment. The UAV must visit a set of air points in minimum time while respecting energy constraints, relying on the UGV as a mobile charging station. Unlike prior work that assumed deterministic travel times or used fixed robustness margins, we model travel times as random variables and bound the probability of failure (energy depletion) across the entire mission to a user-specified risk level. We formulate the problem as a Mixed-Integer Program and propose PRO-SPECT, a polynomial-time algorithm that generates risk-bounded plans. The algorithm supports both offline planning and online re-planning, enabling the team to adapt to disturbances while preserving the risk bound. We provide theoretical results on solution feasibility and time complexity. We also demonstrate the performance of our method via numerical comparisons and simulations.

Figures & tables

Panel of Figure 1 — Fig. 1 : Offline plan generated by PRO-SPECT : (a) $\mathcal{P}_{\text{UAV}}$ ; (b) TSP solution for $\mathcal{S}$ with $x_{0}$ (lower left) and $x_{\text{f}}$ (upper right); (c) tour construction via dynamic programming with UGV path (gray) and UAV tours (blue).

Parameter	Value	Parameter	Value
$x_{0}$ (Initial point)	$(0,0,0)$	$x_{\text{f}}$ (Final point)	$(4000,4000,0)$
$\bar{\tau}_{a}$ (Max flight time)	$600$ s	$\gamma$ (Recharge ratio)	$1$

TABLE I : Mission Parameters for Numerical Evaluations

$\boldsymbol{n}$	Comp. Time (s)	Parallel Comp. Time (s)	$\boldsymbol{\tau(X)}$ (s)
25	$8.1\pm 0.21$	$4.7\pm 1.2$	$5400\pm 670$
50	$120\pm 1.1$	$25\pm 6.5$	$6500\pm 570$
75	$850\pm 1.6$	$110\pm 31$	$7600\pm 560$
100	$2800\pm 7.5$	$330\pm 14$	$8200\pm 510$

TABLE II : PRO-SPECT Comp. Time and Mission Time,

\tau(X)

, Varying

n

$\boldsymbol{n}$	$\boldsymbol{p_{r}}$ (user-specified)
$\boldsymbol{n}$	0.01	0.10	0.20	0.50
25	$0.0001$	$0.018$	$0.018$	$0.10$
50	$0.0007$	$0.011$	$0.011$	$0.033$
75	$0.0005$	$0.015$	$0.024$	$0.11$
100	$0.0001$	$0.0061$	$0.0061$	$0.11$

TABLE III : PRO-SPECT Mean Empirical Failure Rate,

\hat{p}_{r}

, Varying

n

and

p_{r}

$\boldsymbol{n}$	Offline		Online
$\boldsymbol{n}$	$\boldsymbol{\hat{p}_{r}}$	$\boldsymbol{\hat{\tau}(X)}$ (s)	$\boldsymbol{\hat{p}_{r}}$	$\boldsymbol{\hat{\tau}(X)}$ (s)
20	$0.012$	$5300\pm 650$	$\boldsymbol{0}$	$\boldsymbol{5100\pm 510}$
30	$0.020$	$5800\pm 760$	$\boldsymbol{0}$	$5800\pm 1000$
40	$0.0058$	$\boldsymbol{5800\pm 420}$	$\boldsymbol{0.004}$	$6200\pm 560$
50	$0.011$	$6500\pm 570$	$\boldsymbol{0}$	$6500\pm 450$

TABLE IV : PRO-SPECT Offline vs. Online: Empirical Failure Rate,

\hat{p}_{r}

, and Empirical Successful Mission Time,

\hat{\tau}(X)

, for

p_{r}=0.1

and Varied

n

$\boldsymbol{n}$	Branch and Cut		PRO-SPECT
$\boldsymbol{n}$	Comp. Time (s)	$\boldsymbol{\tau(X)\text{ (s)}}$	Comp. Time (s)	$\boldsymbol{\tau(X)\text{ (s)}}$
2	$0.43\pm 0.36$	$\boldsymbol{2400\pm 140}$	$\boldsymbol{0.0051\pm 0.0007}$	$2900\pm 640$
3	$3.0\pm 1.3$	$\boldsymbol{2800\pm 510}$	$\boldsymbol{0.0075\pm 0.0016}$	$3100\pm 660$
4	$18\pm 14$	$\boldsymbol{3500\pm 900}$	$\boldsymbol{0.015\pm 0.0049}$	$3700\pm 980$

TABLE V : Branch and Cut vs. PRO-SPECT: Computation Time and Mission Time,

\tau(X)

, Varying

n

$\boldsymbol{T_{\text{max}}}$	Comp. Time (s)			$\boldsymbol{\tau(X)}$ (s)
	Steps			Steps
	50k	100k	150k	50k	100k	150k
500	$40\pm 1.5$	$40\pm 3.7$	$41\pm 3.5$	$8700\pm 1200$	$9100\pm 1300$	$8700\pm 1100$
1000	$80\pm 14$	$80\pm 11$	$79\pm 8.2$	$7900\pm 830$	$7800\pm 1300$	$8300\pm 1100$
1500	$120\pm 7.0$	$110\pm 9.8$	$120\pm 8.4$	$7700\pm 1000$	$7700\pm 1100$	$8000\pm 820$

TABLE VI : Simulated Annealing Average Computation Time and Mission Time,

\tau(X)

, Varying

T_{\text{max}}

and Number of Steps

$\boldsymbol{n}$	TERRA			PRO-SPECT
$\boldsymbol{n}$	Comp. Time (s)	$\boldsymbol{\tau(X)}$ (s)	$\boldsymbol{\hat{p}_{r}}$	Comp. Time (s)	$\boldsymbol{\tau(X)}$ (s)	$\boldsymbol{\hat{p}_{r}}$
25	$\boldsymbol{0.017\pm 0.0069}$	$12000\pm 1100$	$0.076$	$4.0\pm 0.21$	$\boldsymbol{6200\pm 500}$	0.0095
50	$\boldsymbol{0.09\pm 0.044}$	$16000\pm 1400$	$0.31$	$68\pm 2.7$	$\boldsymbol{6900\pm 780}$	0.014
75	$\boldsymbol{0.31\pm 0.23}$	$19000\pm 1600$	$0.68$	$380\pm 6.5$	$\boldsymbol{7600\pm 790}$	0.014
100	$\boldsymbol{0.82\pm 0.37}$	$22000\pm 1900$	$0.85$	$1300\pm 14$	$\boldsymbol{8600\pm 480}$	0.0013

TABLE VII : TERRA vs. PRO-SPECT: Computation Time, Mission Time,

\tau(X)

, and Empirical Failure Rate,

\hat{p}_{r}

, Varying

n

$\boldsymbol{p_{r}}$	$\boldsymbol{n}$	RSPECT			PRO-SPECT
$\boldsymbol{p_{r}}$	$\boldsymbol{n}$	Comp. Time (s)	$\boldsymbol{\tau(X)}$ (s)	$\boldsymbol{\hat{p}_{r}}$	Comp. Time (s)	$\boldsymbol{\tau(X)}$ (s)	$\boldsymbol{\hat{p}_{r}}$
0.01	25	$\boldsymbol{0.057\pm 0.012}$	$5900\pm 750$	0	$6.6\pm 0.11$	$\boldsymbol{5800\pm 720}$	$0.0001$
	50	$\boldsymbol{0.16\pm 0.017}$	$7100\pm 640$	0	$140\pm 8.8$	$\boldsymbol{6700\pm 530}$	$0.0021$
	75	$\boldsymbol{0.32\pm 0.048}$	$8100\pm 490$	0.0006	$790\pm 2.5$	$\boldsymbol{7700\pm 440}$	$0.0010$
	100	$\boldsymbol{0.52\pm 0.098}$	$9000\pm 600$	$0.0013$	$3300\pm 33$	$\boldsymbol{8400\pm 640}$	0.0003
0.1	25	$\boldsymbol{0.055\pm 0.012}$	$5800\pm 590$	$0.025$	$8.1\pm 0.21$	$\boldsymbol{5400\pm 670}$	0.018

TABLE VIII : RSPECT vs. PRO-SPECT: Comp. Time, Mission Time,

\tau(X)

, and Empirical Failure Rate,

\hat{p}_{r}

, Varying

n

p_{r}

Parameter	Value	Parameter	Value
$x_{0}$ (Initial point)	$(0,0,0)$	$x_{\text{f}}$ (Final point)	$(40,40,0)$
$\bar{\tau}_{a}$ (Max flight time)	$60$ s	$\gamma$ (Recharge ratio)	$1$
$\bar{w}_{x},\bar{w}_{y}$ (Max wind speed, x, y)	$1$ m/s	$\bar{w}_{z}$ (Max wind speed, z)	$0.3$ m/s
$[\underline{v}_{a},\overline{v}_{a}]$ (UAV speed)	$[1.5,2]$ m/s	$[\underline{v}_{g},\overline{v}_{g}]$ (UGV speed)	$[0.15,0.25]$ m/s

TABLE IX : Mission Parameters for Simulations

Fig. 2 : Simulation setup. (a) UAV-UGV team in the simulated environment. (b) Simulated wind field applied to the UAV, with arrow direction and magnitude indicating local wind velocity.

Panel of Figure 12 — Fig. 3 : Mission Plan in ROS Simulation with Online Replanning: ( 3a ) at mission start, ( 3b ) partway through second tour, and ( 3c ) at mission end. Green triangle denotes UAV location and bold edge denotes next transit.

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Robust and Scalable UAV-UGV Planning for Aerial Monitoring under Energy and Precedence Constraints

Cahit Ikbal Er, Yasin Yazicioglu

Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA · Departments of Mechanical and Industrial Engineering and Electrical and Computer Engineering, Northeastern University, Boston, MA, USA

Constrained Motion Planning Vehicle Routing Multi-Robot Coordination

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We consider planning for unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) teams in aerial monitoring missions with ordering requirements on the monitoring points to be visited by the UAV. The system consists of multiple UAV-UGV teams, each comprising one UAV and one UGV. UAV energy limitations are modeled through endurance, defined as the maximum flight time on a full battery. The UGVs serve as mobile charging stations and transport the UAVs between consecutive aerial tours. Given a set of monitoring points subject to ordering constraints and the teams' initial and terminal positions, the objective is to minimize mission completion time while satisfying UAV energy limits and the required visit order under bounded travel-time disturbances that may arise during execution. Unlike prior work, the plan jointly determines vehicle routes and their timing, allowing teams to slow down as needed to satisfy the ordering constraints. We develop a polynomial-time algorithm that generates efficient solutions to the underlying NP-hard planning problem. We establish feasibility guarantees, characterize the algorithm's computational complexity, and evaluate its performance via numerical comparisons.

Abstract

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