ARL-TR-8042 ● JUNE 2017

US Army Research Laboratory

Assessment of Energy-Efficient and ModelBased Control

by Craig Lennon, Marshal Childers, Mario Harper, 

Camilo Ordonez, Nikhil Gupta, James Pace, Ryan Kopinsky,

Aneesh Sharma, Emmanuel Collins, and Jonathan Clark

Approved for public release; distribution is unlimited.
NOTICES 

Disclaimers

The findings in this report are not to be construed as an official Department of the 

Army position unless so designated by other authorized documents.

Citation of manufacturer’s or trade names does not constitute an official 

endorsement or approval of the use thereof.

Destroy this report when it is no longer needed. Do not return it to the originator.
ARL-TR-8042 ● JUNE 2017

US Army Research Laboratory

Assessment of Energy-Efficient and ModelBased Control

by Craig Lennon and Marshal Childers

Vehicle Technology Directorate, ARL

Mario Harper, Camilo Ordonez, Nikhil Gupta, James Pace, 

Ryan Kopinsky, Aneesh Sharma, Emmanuel Collins, and 

Jonathan Clark

Center for Intelligent Systems, Controls and Robotics, Jointly 

Sponsored by Florida A&M University and Florida State University, 

Tallahassee, FL

Approved for public release; distribution is unlimited.
ii

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently 

valid OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

June 2017

2. REPORT TYPE

Technical Report

3. DATES COVERED (From - To)

June 2016

4. TITLE AND SUBTITLE

Assessment of Energy-Efficient and Model-Based Control

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Craig Lennon, Marshal Childers, Mario Harper, Camilo Ordonez, Nikhil Gupta, 

James Pace, Ryan Kopinsky, Aneesh Sharma, Emmanuel Collins, and 

Jonathan Clark

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

US Army Research Laboratory

Autonomous Systems Division

Vehicle Technology Directorate (ATTN: RDRL-VTA)

Aberdeen Proving Ground, MD 21005-5069.

8. PERFORMING ORGANIZATION REPORT NUMBER

ARL-TR-8042

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)

11. SPONSOR/MONITOR'S REPORT NUMBER(S)

12. DISTRIBUTION/AVAILABILITY STATEMENT

Approved for public release; distribution is unlimited.

13. SUPPLEMENTARY NOTES

14. ABSTRACT

The US Army Research Laboratory’s (ARL’s) Robotics Collaborative Technology Alliance is a program intended to change 

robots from tools that Soldiers use into teammates with which Soldiers can work. One desired ability of such a teammate is 

the ability to operate in an energy-efficient manner on a variety of surfaces. To develop such a teammate, alliance researchers

developed planning algorithms that incorporate knowledge of the vehicle’s steering and control system. These algorithms 

adapt their navigation to different types of terrain, learning appropriate parameter values by conducting a brief set of trial 

maneuvers, and are intended to enable the robot to operate in a manner that is more energy efficient. In June of 2016, ARL

researchers conducted an assessment of this technology by comparing this planning algorithm to a traditional minimumdistance planning algorithm. This assessment found an overall improvement in energy efficiency, which was clearly visible 

when the systems operated on grass, but unclear when the systems operated on asphalt. Overall, the results suggest that the 

energy-efficient planner does have the potential to plan more energy-efficient paths.

15. SUBJECT TERMS

unmanned ground system, autonomous systems, robotics, mobility, planning, energy

16. SECURITY CLASSIFICATION OF:

17. LIMITATION

 OF

 ABSTRACT

UU

18. NUMBER

 OF 

 PAGES

30

19a. NAME OF RESPONSIBLE PERSON

Craig Lennon

a. REPORT

Unclassified

b. ABSTRACT

Unclassified

c. THIS PAGE

Unclassified

19b. TELEPHONE NUMBER (Include area code)

410-278-9886

Standard Form 298 (Rev. 8/98)

Prescribed by ANSI Std. Z39.18
Approved for public release; distribution is unlimited.

iii

Contents

List of Figures iv

List of Tables iv

1. Introduction 1

2. Robotic System 1

2.1 Robotic Platform 1

2.2 Dynamically Feasible Energy-Efficient Motion Planning 2

2.3 Learning of Terrain-Dependent Models 2

2.4 Purpose of the Experiment 3

3. Experimental Design 3

4. Results 6

4.1 Energy and Collision 6

4.2 Re-planning and Time 12

4.3 Outliers and Model Checking 15

5. Conclusions 16

6. References 18

Appendix. Data from Runs 19

List of Symbols, Abbreviations, and Acronyms 23

Distribution List 23
Approved for public release; distribution is unlimited.

iv

List of Figures

Fig. 1 ClearPath Husky used for the assessment. The upper camera (A) was 

used for visual odometry, and the lower (B) was not used at all. The 

lidar (C) was used for obstacle avoidance. ........................................... 2

Fig. 2 Representative course layout. The goal position is marked by an 

orange cone. .......................................................................................... 4

Fig. 3 Density of difference in energy expenditure within configurations by 

terrain .................................................................................................... 8

Fig. 4 Energy expenditure by terrain and planning type ................................. 9

Fig. 5 Boxplot of aggregate energy use by terrain .......................................... 9

Fig. 6 Number of tracking re-plans by planning type ................................... 13

Fig. 7 Number of collision re-plans by planning type................................... 14

Fig. 8 Time to complete the course by planner type ..................................... 15

Fig. 9 Normal Q–Q plot of differences in energy expended for each 

configuration. The line shows the path a normal distribution would 

follow. ................................................................................................. 16

List of Tables

Table 1 Variables and factors............................................................................. 4

Table 2 Design for the experiment..................................................................... 5

Table 3 Differences in energy expenditure by configuration ............................ 7

Table 4 Results of t-tests of actual energy use................................................... 8

Table 5 ANOVA results................................................................................... 10

Table 6 Collisions by planner and terrain, with x/y indicating collisions in x 

out of y runs........................................................................................ 12

Table 7 Collision results matched for each configuration ............................... 12

Table 8 Differences in actual energy by energy-efficient planning with and 

without learning .................................................................................. 12

Table 9 Re-plans by terrain and planner.......................................................... 14

Table A-1 Recorded data from all runs................................................................ 20

Table A-2 Definitions for all recorded variables ................................................. 21
Approved for public release; distribution is unlimited.

1

1. Introduction

The US Army Research Laboratory’s (ARL’s) Robotics Collaborative Technology 

Alliance (RCTA) is an alliance of robotics research institutions working together 

to transform robots from tools that Soldiers use into teammates with which Soldiers 

can work. One desired ability of such a teammate is the ability to plan motion over 

a variety of surfaces in a manner that conserves energy. To further research into 

this capability, researchers from Florida State University and Carnegie Mellon 

University developed planning algorithms that select routes based on terrain and 

the vehicle’s motor system. In practice, the robot learns appropriate parameter 

values by conducting a set of trial maneuvers and then uses these parameters for 

energy-efficient path planning.

In June of 2016, these capabilities were assessed at Florida State University. The 

assessment consisted of learning terrain parameters for asphalt and grass, and then 

navigating a path through obstacles on a flat patch of grass or asphalt. In Section 2, 

we describe the integrated system and the algorithm that was assessed. Section 3 

describes the methodology of the assessment, Section 4 presents the assessment 

results, and Section 5 contains our conclusions.

2. Robotic System

In this section, we describe the equipment and technology that played a key role in

the assessment. We start with the robotic platform, including the sensors and 

computational power, followed by a description of the planning and learning 

algorithms.

2.1 Robotic Platform

The robot used in the integrated assessment is a Clearpath Husky, equipped with 3

Mac Mini machines, each with 2.3 GHz quad-core processors, used for hardware 

control, planning, maintaining a map of the environment, and communicating with 

the user. A fourth computer with a 1.2 GHz Intel Core 2 DUO processor ran a visual 

odometry algorithm. The input for the visual odometry was provided by the upper, 

and downward facing, Bumblebee 2 stereo camera shown in Fig. 1. A Hokuyo lidar 

was used for obstacle detection. Linear Hall effect sensors were attached to each of 

the motor’s sides to measure wheel speed for the learning phase.
Approved for public release; distribution is unlimited.

2

Fig. 1 ClearPath Husky used for the assessment. The upper camera (A) was used for visual 

odometry, and the lower (B) was not used at all. The lidar (C) was used for obstacle avoidance.

2.2 Dynamically Feasible Energy-Efficient Motion Planning

Skid-steer robots are commonly used as robotic platforms because they are simple 

and robust. But in order to turn, the wheels of such a vehicle must skid or slip, a 

terrain-dependent action that complicates localization.1 Sharp turns may also 

require motor torque in excess of what the vehicle can provide, which can lead to 

route re-planning and wasted energy.1 Gupta et al.2 proposed a method of planning 

that constrains paths to those that are dynamically feasible given a terrain type, 

payload, and vehicle model. It does so by estimating the required torque for a turn 

given the terrain, and then sampling possible path extensions, rejecting those that

demand torque in excess of what the vehicle could provide. This search is guided 

by a heuristic with a preference for energy-efficient paths. To estimate the torque 

required for a turn, the model requires the setting of parameters related to the 

platform structure and mass, and the resistive forces of friction. That means that 

given a known, skid-steered platform and known payload, the model requires only 

parameters depending on terrain type.

2.3 Learning of Terrain-Dependent Models

The robot begins with a kinematic and a friction model that has been learned based 

on a theoretical model and prior navigation. When the robot faces new terrain, the 
Approved for public release; distribution is unlimited.

3

system drives along a diagnostic path, varying speed and turning radii. The robot 

then updates its previously learned models based on its more recent navigation 

experience. The physical experiments to date have been conducted on flat terrain.

The theoretical model in Gupta et al.2 was constructed to support navigation on a 

plane with constant slope, although physical experiments have been conducted only 

on terrain with zero or negligible slope. For terrain with varying slope, the terrain 

could likely be approximated by the robot as a union of segments of planes, each 

with constant slope, and with the sampling algorithm choosing sample paths within 

plane segments. Alternatively, an approximate plane could be fit to the terrain, the 

path calculated on the approximate path, and then executed on the actual terrain. In 

this case, areas of actual terrain with the greatest difference from the approximated 

plane could be avoided by using the residuals of the fit as part of the planning 

heuristic.

2.4 Purpose of the Experiment

These algorithms have been integrated with the RCTA world model3 that is 

examined in Lennon et al.,4 so that learning of terrain models and energy-efficient 

motion planning can be performed online by the RCTA system. This experiment 

was intended to compare minimum distance motion planning with the energyefficient planning method from Ordonez et al.1 to determine if the latter was more 

energy efficient. A secondary purpose was to verify that the learning process of 

Section 2.3 does improve the planning described in Section 2.2.

3. Experimental Design

The design of the experiment was effected substantially by environmental 

conditions. A sudden tropical storm brought rain during the week of the assessment, 

with the result that the assessment needed to be compressed into 1 day to avoid the 

rain. This limited the number of runs we could conduct, but did not change the basic 

structure of the experiment. The assessment consisted of navigation over a flat 

patch of asphalt or grass, with a series of obstacles placed on it. The key factors and 

variables are listed in Table 1. If more time had been available, more terrain types 

would have been included. The terrain type was not originally thought to be a factor 

related to planner performance, but only a source of variation in performance, along 

with obstacle configuration. Obstacle configurations were not kept the same 

between the grass and asphalt configurations, because this would have required 

more time to carefully place obstacles, and we believed that this time was better

spent by getting in more runs.
Approved for public release; distribution is unlimited.

4

Table 1 Variables and factors

Factor/Variable Levels

Planning type Minimum distance, energy efficient, energy efficient without learning

Terrain Asphalt, grass

Obstacles Configurations of obstacles were treated as blocks

Energy used The energy in joules used during the run (continuous variable)

Collisions Count of the number of collisions with obstacles (whole number)

The terrain types considered were asphalt and grass, and the obstacles were 

cardboard cylinders that the robot would need to steer around. Each separate 

configuration of cylinders was treated as a block, with the intent of examining the 

difference in performance of the algorithms within each block. Since the primary 

purpose was to compare energy-efficient planning with learning against minimumdistance planning, the planning type was kept at 1 of these 2 levels for 32 out of the 

36 runs. The overall number of runs (36) was determined by the time restrictions.

An example of a set up course is shown in Fig. 2, and the design is shown in Table 2. 

In this table, configuration refers to a given setup of barrels, and the algorithm 

values are: minimum distance (MD), energy efficient (EE), and energy efficient 

without learning parameter values (EE Default). The intent was to allow a 

comparison between the amount of energy used by the minimum-distance and 

energy-efficient planners within each block. This would provide 16 comparison 

values to assess the difference between the minimum-distance and energy-efficient 

planners, and 4 comparison values for energy-efficient planning with and without 

learning. The order of the algorithms was randomized within the blocks. We did 

not originally intend to compare the performance of the planners by terrain type.

Fig. 2 Representative course layout. The goal position is marked by an orange cone.
Approved for public release; distribution is unlimited.

5

Table 2 Design for the experiment

Run Terrain Configuration Planning algorithma

1 Asphalt 1 MD

2 Asphalt 1 EEP

3 Asphalt 2 EEP

4 Asphalt 2 MD

5 Asphalt 3 EEP

6 Asphalt 3 MD

7 Asphalt 4 EEP

8 Asphalt 4 MD

9 Asphalt 5 EEP

10 Asphalt 5 MD

11 Asphalt 6 MD

12 Asphalt 6 EEP

13 Asphalt 7 MD

14 Asphalt 7 EE Default

15 Asphalt 7 EEP

16 Asphalt 8 EE Default

17 Asphalt 8 MD

18 Asphalt 8 EEP

Change locations

Run Terrain Configuration Algorithm

19 Grass 9 EEP

20 Grass 9 MD

21 Grass 10 MD

22 Grass 10 EEP

23 Grass 11 MD

24 Grass 11 EEP

25 Grass 12 MD

26 Grass 12 EEP

27 Grass 13 MD

28 Grass 13 EEP

29 Grass 14 EEP

30 Grass 14 MD

31 Grass 15 EEP

32 Grass 15 EE Default

33 Grass 15 MD

34 Grass 16 EE Default

35 Grass 16 MD

36 Grass 16 EEP a Algorithm was minimum distance (MD), energy efficient (EE), or energy efficient without terrain learning 

(EE Default).
Approved for public release; distribution is unlimited.

6

The most important dependent variable was the actual energy expended during the 

run, but the following were also recorded:

• whether a collision occurred

• time taken to finish the run (Time)

• number of times re-planning occurred to avoid collision (CollisionReplan)

• number of times tracking re-planning occurred. These re-plans are generally 

caused by localization error because of issues with perception, slipping, or 

skidding (TrackingReplan)

The Appendix includes recorded data from all runs (Table A-1) and all variables 

and their definitions are listed in Table A-2.

The expectation was that with energy-efficient planning, CollisionReplan and 

TrackingReplan should be no greater than the number of such occurrences under 

minimum-distance planning, and that time should not differ substantially between 

the 2 planning methods. These comparisons were not central to the experiment, and 

we planned to subject them only to exploratory data analysis, without any direct 

testing.

4. Results

The experiment occurred on June 7, 2016, during a break in a tropical storm, with 

the runs on the asphalt lasting from about 0900 to 1200, and the runs on the grass 

lasting from about 1300 to 1600. We break our examination of results into 

subsections, with the first being a comparison of the 2 planners with respect to the 

difference in energy expenditure and the difference in the number of collisions with 

obstacles. The second is an exploration of the time required to complete the course 

and the number of re-planning attempts.

4.1 Energy and Collision

The experiment was designed to compare minimum-distance and energy-efficient 

planning on the basis of the energy expended (in joules). For energy expended, we 

intended to look at each configuration and consider the difference in energy usage 

between the 2 planning methods. We had originally considered using a paired t-test 

to examine the significance of the differences; however, we found that the 

variability of performance of the planners, possibly due to perception, made the 

power of such a test low. The results of Gupta et al.2 suggested an energy savings 

of 30%–40% might be possible on inclined planes, and the expectation was that an 
Approved for public release; distribution is unlimited.

7

energy savings of no more than that would be possible on a flat surface with a real 

system. Given such a savings, a paired t-test with 16 pairs, and with the variance 

actually observed, would have had a power of 0.99, thus failing to appropriately 

reject a null hypothesis of equality with probability 0.01 (at a 0.05 level of 

significance). However, if the energy saving was only 10%, the power would drop 

to 0.8, meaning we would fail to detect a true difference in the means with a 

probability of 0.2. Some of the variability in performance could be attributable to 

the performance of the algorithms with different terrain configurations. We cannot 

neglect the possibility, however, that some performance differences are due to 

perception errors—particularly in the extreme cases we discuss in Section 4.3. This 

added variability in performance would make it more difficult to detect a true 

difference in energy savings and would lower the power of the test. Thus, while we 

included the results of the originally planned paired t-tests, we are inclined to give 

more weight to the confidence intervals, and in particular to the confidence intervals 

with the extreme values removed. The difference in energy use between the 2

planners is listed in Table 3 and the results of the previously mentioned tests are in 

Table 4.

Table 3 Differences in energy expenditure by configuration

Configuration Difference 

(MD–EE) Terrain

1 88.34 Asphalt

2 –876.61 Asphalt

3 –974.22 Asphalt

4 26.59 Asphalt

5 2,919.41 Asphalt

6 –166.71 Asphalt

7 138.96 Asphalt

8 1,453.43 Asphalt

9 –971.19 Grass

10 –828.91 Grass

11 –2,775.33 Grass

12 –922.88 Grass

13 –2,819.5 Grass

14 –5,394.35 Grass

15 1,033.75 Grass

16 –344.33 Grass
Approved for public release; distribution is unlimited.

8

Table 4 Results of t-tests of actual energy use

All observations Extremes removed

Number of pairs 16 14

p-value 0.13 0.06

Confidence interval for EE 

planner energy savings (–262, 1812) joules (–39, 1458) joules

Average savings for the 

energy-efficient planner 775 joules 710 joules

We also found that we needed to consider the possibility of a difference by terrain 

type. During exploratory data analysis, we noticed a difference in planner 

performance on grass and asphalt. The density of the differences in energy 

expenditure are shown in Fig. 3, separately for grass and asphalt. The amount of 

energy expended by each planner on each run is shown in Fig. 4. As shown in 

Figs. 3 and 4, the performance of the energy efficient planning seemed to be 

superior on grass, but no difference is discernable on asphalt. There was also a 

noticeable difference between the overall amount of energy expended on grass and 

on asphalt, with runs on asphalt using more energy than those on grass, as shown 

in Fig. 5.

Fig. 3 Density of difference in energy expenditure within configurations by terrain
Approved for public release; distribution is unlimited.

9

Fig. 4 Energy expenditure by terrain and planning type

Fig. 5 Boxplot of aggregate energy use by terrain
Approved for public release; distribution is unlimited.

10

We conducted the planned 2-sided t-test with a null hypothesis of no difference in 

the mean of actual energy expenditure between the 2 planners. This test neglects 

terrain and considers all differences as a sample from a single distribution. From 

this test, we obtained a p-value of 0.1319 and a 95% confidence interval of –262, 

1812 joules, which represents a confidence interval for the energy that the energyefficient planner would save, on average. In the process of checking our model, 

however, we examined a quantile–quantile (Q–Q) comparison with a normal 

distribution, shown in Fig. 8 of Section 4.3. This brought to our attention 2 extreme 

observations that while not in error, deviated substantially from the others. One 

represented the best performance of the energy-efficient planner relative to the 

minimum-distance planner, and one represented the worst performance by the 

energy-efficient planner relative to the minimum-distance planner. We conducted 

the t-test again, with these samples removed, and found that with this modification, 

one would find evidence of a difference between the planners, with a p-value of 

0.06 and a 95% confidence interval from –39, 1458 joules, again representing a 

confidence interval for the energy that would be saved by using the energy-efficient 

planner, on average.

Based on the exploratory data analysis (Fig. 3), and on an examination of the 

collision data, which we will present later in this subsection, we also conducted an 

analysis of variance (ANOVA) to consider the interaction of terrain and planner.

Because of the pairing, we conducted a 2-factor repeated measures ANOVA, 

thinking of each configuration as a subject and each planner as a treatment applied 

to each subject. Thus, the planner is considered a within-subject effect and the 

terrain was considered a between-subjects effect. The results are shown in Table 5 

and provide weak evidence for an interaction of terrain and planner type. While this 

could be due to the actual terrain, it could also represent the inadequate learning of 

the parameters for that terrain type, since parameter learning was conducted only 

at the start of the runs on a given terrain type.

Table 5 ANOVA results

DF Sum square Mean square P value

Terrain 1 1,999,605 1,999,605 0.2950

Planner 1 64,700 64,700 0.8490

Terrain: Planner 1 5,132,349 5,132,349 0.0988

Residuals 26 45,516,174 1,750,622 . . .

With the extremes of performance of the energy-efficient planner removed, there is 

evidence of an energy saving advantage to energy-efficient planning. Even with the 

extremes, however, the confidence intervals of Table 4, suggest that, if energyefficient planning and minimum-distance planning use equal resources to perform, 
Approved for public release; distribution is unlimited.

11

one might expect, on average, to achieve energy savings from the energy-efficient 

planner. These confidence intervals are more informative than the p-value of the 

test because over a course of such short length there is unlikely to be a great 

difference in energy expenditure, making a difference between the planners 

difficult to detect, especially with variability added by other factors. Indeed, for the 

probability of falsely rejecting the null hypothesis to be equal to the probability of 

incorrectly failing to reject the null hypothesis (power of 0.9 at a significance level 

of 0.1), the energy-efficient planner would have needed a mean energy savings of 

1210 joules (20% over) the minimum-distance planner, which is likely difficult to 

obtain over a course with a length of 10 m.

In path planning, obstacle avoidance can be achieved by placing a buffer around 

detected obstacles, and prohibiting the planner from planning a path within the 

buffered area. The smaller the buffer, the greater the likelihood of collision, and the 

larger the buffer, the less space available for planning paths. In this experiment, this 

buffer was set to be small, allowing for more flexibility in planning paths, but 

greater likelihood of collision. Therefore, although several collisions occurred with 

the minimum-distance planner, such collisions are not inherent to minimumdistance planning, and could be avoided with greater constraints on the planner, 

which would presumably result in longer paths and higher energy use. However, 

since both planners used the same buffer around objects, we considered it 

reasonable to compare them based on these criteria.

When, during the course of a run the robot touched an obstacle, the robot’s starting 

coordinates were checked to make sure that no error was caused by drift over the 

course of the experiment. If the starting coordinates were incorrect, the robot was 

rebooted and the run repeated. If the coordinates were accurate, a collision was 

recorded and the run counted. Table 6 shows the number of collisions by planner 

and terrain, and these results suggest an interaction of terrain and planner. Table 7 

shows the collision totals by planner type. While we cannot be certain of the reasons 

behind the greater number of collisions on the grass, the results of Table 6 and Figs. 

4 and 5 suggest a plausible reason: the grass was slippery and the asphalt was not.

Slippery grass would make collisions more likely (Table 6) and would make turns 

less energy intensive, leading to less energy use on the grass (Fig. 4). Moreover, 

this slipperiness would be taken into account by the energy-efficient planner, after 

its learning phase, and not by the minimum-distance planner.
Approved for public release; distribution is unlimited.

12

Table 6 Collisions by planner and terrain, with x/y indicating collisions in x out of y runs

Terrain/planning method Min distance Energy efficient

Grass 5/8 0/8

Asphalt 0/8 0/8

Table 7 Collision results matched for each configuration

Energy efficient

Minimum 

distance

Collision No collision

Collision 0 5

No collision 0 11

We consider the combination of Tables 4 and 5 as evidence of a potential advantage 

of the energy-efficient planner on the grass, and possibly on other slippery terrain.

The advantage is not in avoiding collisions—which could be done by buffering 

around obstacles—but in planning paths that avoid them without such buffering, 

which represents a possible advantage because such buffering sometimes has the 

effect of making traversable paths appear untraversable. 

As a secondary goal, we wanted to verify that the learning process improved the 

performance of the energy-efficient planner. Considering the 4 configurations in 

which this comparison was made, a paired t-test of the actual energy expended 

provides evidence for rejecting the hypothesis that the mean energy expended is 

equal in favor of the alternative hypothesis that the difference in the means is not

equal to 0 (p-value 0.06), with a 95% confidence interval of (–137, 2664) for the 

mean-energy savings gained by learning before using the energy-efficient 

algorithm. The actual values for these 4 runs are in Table 8.

Table 8 Differences in actual energy by energy-efficient planning with and without 

learning

Configuration Without learning–With learning

(joules)

7 –914

8 –2492

15 –457

16 –1153

4.2 Re-planning and Time

Having made the comparisons for which the experiment was conducted, we briefly 

explore some secondary concerns: differences in re-planning and in time taken to 
Approved for public release; distribution is unlimited.

13

complete the course. Figures 6 and 7 are boxplots comparing the distributions of 

the number of re-plans due to trajectory corrections (tracking) and for the purpose 

of collision avoidance (collision). These plots show that the average number of 

tracking re-plans was similar, but that the distance planner needed a greater number 

of collision avoidance re-plans. Fewer collision avoidance re-plans suggests a more 

reasonable choice of path, but we note that a gain in time from fewer re-plans may 

be balanced by longer time taken to make the plan. No data were collected to 

examine this because the tradeoff between frequent-but-hasty planning versus 

better-but-lengthier planning was not an important aspect of the experiment. Table 

9 provides the average number of re-plans by planner, type of re-plan, and terrain,

as well as the average length of time to complete the course by terrain and planner 

type. This table, along with a plot of the completion times in Fig. 8, suggest that the 

route chosen by energy-efficient planning does not necessarily take longer to 

complete than that chosen by minimum-distance planning; although the added time

due to collisions and the short courses involved make us wary of drawing much 

from the completion time data. The re-planning and time data provide no evidence 

of worse performance by the energy-efficient planner.

Fig. 6 Number of tracking re-plans by planning type
Approved for public release; distribution is unlimited.

14

Fig. 7 Number of collision re-plans by planning type

Table 9 Re-plans by terrain and planner

Terrain Planner Average no.

tracking re-plans

Average no.

collision re-plans

Time 

(s)

Grass Distance 5.1 9.0 25.1

Energy 4.0 6.7 24.0

Asphalt Distance 3.6 10.5 24.9

Energy 4.1 6.3 24.1
Approved for public release; distribution is unlimited.

15

Fig. 8 Time to complete the course by planner type

4.3 Outliers and Model Checking

In examining Table 4, the results from configuration 5 stood out from the other 

asphalt runs, and the results of configuration 14 stood out from the other grass runs.

Consequently, we re-examined the video from these runs to see if anything unusual 

effected the results. We found nothing unusual in the runs. In configuration 5, the 

energy-efficient planner just chose a longer route to avoid sharper turns, and paid a 

price in energy consumption for it. Likewise, in configuration 14 the choice of the 

energy-efficient planner simply paid off better, both in energy saved and in 

avoiding barrel collisions. In either case, the odd choice of path could have been 

influenced by perceptual errors or by errors in other parts of the system.

Our use of the paired t-test for analysis assumes that the differences in energy 

expended by the minimum-distance and energy-efficient planners are

approximately normally distributed. Figure 9 shows a normal Q–Q plot of these 

differences. The assumption of normality seems appropriate, although the 2

configurations mentioned previously deviate significantly from the line 

representing a normal distribution.
Approved for public release; distribution is unlimited.

16

Fig. 9 Normal Q–Q plot of differences in energy expended for each configuration. The line 

shows the path a normal distribution would follow.

In Section 4.1, we conducted tests to determine whether we should expect a 

difference in mean energy use between the 2 planners. We conducted these tests 

using all pairs of runs, excluding the extreme values represented by configurations 

5 and 14. The exclusion of these values does not mean they are in error and a review 

of the video suggests no measurement error in them; they simply represent extreme 

failures of the energy-efficient/minimum-distance planners in configurations 5 and 

14. Such occasional failures are common in robotics and could represent failures 

by other aspects of the system—for example, perception or localization. 

While the results with and without extreme values differ in their p-values, the 

confidence intervals are similar and both suggest that on average, energy-efficient 

planning really is more energy efficient as compared with the minimum-distance 

planner used for these tests.

5. Conclusions

The energy-efficient planning proposed in Ordonez et al.1 and Gupta et al.2 showed

promise—demonstrating superior performance on grass, navigating with fewer 

collisions, and expending less energy on average. There was not a clear difference 

on asphalt, however. Overall, there is evidence to suggest that on average, energyefficient planning will save energy—at least by comparison with the version of 

minimum-distance planning with which it was compared here. It would be 

beneficial to examine the differences in performance when the platforms operate 
Approved for public release; distribution is unlimited.

17

on slopes, where energy-efficient planning could be expected to have substantially 

greater performance. The test courses were small but it is reasonable to expect that 

the advantages in energy expenditure may hold up on a larger scale, provided a map 

is available for the energy-efficient planner to use. On a larger scale, however, the 

assumption that terrain can be approximated by a plane would not be reasonable 

and an extension of the algorithm will be required for this situation. We would 

expect that on a more cluttered course, with a good map, the energy-efficient 

planner would have a greater advantage, while a course that is more open, or one 

without an available map, would reduce or eliminate the advantages of energyefficient planning.
Approved for public release; distribution is unlimited.

18

6. References

1. Ordonez C, Gupta N, Reese B, Seegmiller N, Kelly A, Collins E. Learning of 

skid-steered kinematic and dynamic models for motion planning. Robotics and

Autonomous Sys. 2015. 

2. Gupta N, Ordonez C, Collins E. Dynamically feasible, energy efficient motion 

planning for skid-steered vehicles. Autonomous Robots. 2016:1–19.

3. Dean R. Common world model for unmanned systems. Proc. SPIE; c2013.

4. Lennon C, Bodt B, Childers M, Dean R, Oh J, DiBerardino C, Keegan T. 

RCTA capstone assessment. Proc. SPIE; c2015.
Approved for public release; distribution is unlimited.

19

Appendix. Data from Runs
Approved for public release; distribution is unlimited.

20

Table A-1 Recorded data from all runs

Terrain Block Planner Tracking 

re-plan

Collision 

re-plan

Actual 

energy

Collision Run Time

Asphalt 1 Distance 5 4 6,838.24 No 1 20

Asphalt 1 Energy 4 9 6,926.58 No 2 22

Asphalt 2 Energy 3 6 5,972.92 No 3 30

Asphalt 2 Distance 3 14 7,849.53 No 4 26

Asphalt 3 Energy 6 8 6,651.2 No 5 25

Asphalt 3 Distance 5 18 8,625.42 No 6 26

Asphalt 4 Energy 4 5 7,058.7 No 7 27

Asphalt 4 Distance 2 25 7,032.11 No 8 26

Asphalt 5 Distance 3 4 4,305.44 No 9 26

Asphalt 5 Energy 3 5 7,224.85 No 10 25

Asphalt 6 Distance 5 1 5,211.67 No 11 23

Asphalt 6 Energy* 8 0 4,130.46 No 12 26

Asphalt 6 Energy 5 4 5,044.96 No 13 24

Asphalt 7 Energy* 9 3 3,491.94 No 14 28

Asphalt 7 Distance 3 8 5,844.71 No 15 28

Asphalt 7 Energy 5 0 5,983.67 No 16 24

Asphalt 8 Distance 3 10 5,603.29 No 17 24

Asphalt 8 Energy 3 13 7,056.72 No 18 24

Grass 9 Energy 4 6 4,695.81 No 19 24

Grass 9 Distance 3 14 5,667 Yes 20 NA

Grass 10 Distance 7 1 5,101.76 No 21 23

Grass 10 Energy 5 2 4,272.85 No 22 24

Grass 11 Distance 7 15 6,631.67 Yes 23 26

Grass 11 Energy 6 2 3,856.34 No 24 23

Grass 12 Distance 4 3 3,512.46 No 25 22

Grass 12 Energy 2 6 2,589.58 No 26 21

Grass 13 Distance 5 18 7,472.84 Yes 27 25

Grass 13 Energy 2 15 4,653.34 No 28 22

Grass 14 Energy 4 3 3,530.1 No 29 24

Grass 14 Distance 6 13 8,924.45 Yes 30 28

Grass 15 Energy 6 8 5,079.44 No 31 25

Grass 15 Energy* 6 17 4,622.06 Yes 32 26

Grass 15 Distance 3 7 4,045.69 Yes 33 25

Grass 16 Energy* 6 10 4,651.31 No 34 25

Grass 16 Distance 4 6 6,148.35 No 35 27

Grass 16 Energy 3 11 5,804.02 No 36 29
Approved for public release; distribution is unlimited.

21

Table A-2 Definitions for all recorded variables

Variable Definition

Terrain Type of terrain (grass vs. asphalt)

Block The configuration of barrels

Planner The type of planner used (minimum distance, and energy 

efficient with or without learning)

Tracking re-plan The number of times re-planning was done because the 

trajectory was different from that originally planned

Collision re-plan The number of times re-planning was done because the 

trajectory was different from that originally planned

Actual energy Joules used during the run

HitBarrel Denotes a collision with a barrel (1) or no collisions (0)

Run The number of the run

Time The length of time it took the run to complete
Approved for public release; distribution is unlimited.

22

INTENTIONALLY LEFT BLANK.
Approved for public release; distribution is unlimited.

23

List of Symbols, Abbreviations, and Acronyms

ANOVA analysis of variance

ARL US Army Research Laboratory

EE energy efficient

EE Default energy efficient without terrain learning

MD minimum distance

Q–Q quantile–quantile

RCTA Robotics Collaborative Technology Alliance
Approved for public release; distribution is unlimited.

24

1 DEFENSE TECHNICAL

(PDF) INFORMATION CTR

DTIC OCA

2 DIRECTOR

(PDF) US ARMY RSRCH LAB

RDRL CIO L

IMAL HRA MAIL & RECORDS

MGMT

1 GOVT PRINTG OFC

(PDF) A MALHOTRA

2 DIR USARL

(PDF) RDRL VTA

C LENNON

M CHILDERS