Trajectory Optimization for Quadruped Mobile Manipulators that Carry Heavy Payload Ioannis Dadiotis Arturo Laurenzi and Nikos Tsagarakis

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Trajectory Optimization for Quadruped Mobile Manipulators that

Carry Heavy Payload

Ioannis Dadiotis, Arturo Laurenzi and Nikos Tsagarakis

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Abstract— This paper presents a simpliﬁed model-based tra-

jectory optimization (TO) formulation for motion planning on

quadruped mobile manipulators that carry heavy payload of

known mass. The proposed payload-aware formulation simulta-

neously plans locomotion, payload manipulation and considers

both robot and payload model dynamics while remaining

computationally efﬁcient. At the presence of heavy payload,

the approach exhibits reduced leg outstretching (thus increased

manipulability) in kinematically demanding motions due to

the contribution of payload manipulation in the optimization.

The framework’s computational efﬁciency and performance is

validated through a number of simulation and experimental

studies with the bi-manual quadruped CENTAURO robot

carrying on its arms a payload that exceeds 15 % of its mass

and traversing non-ﬂat terrain.

I. INTRODUCTION

Quadruped robots have in general outperformed wheeled

platforms in rough terrain by taking advantage of their ability

to discretely make and break contact with the environment. In

contrast to aerial robots (which move without contact), they

can, signiﬁcantly, compensate and exert higher interaction

forces due to the legged contact and articulation. This renders

quadruped robots, compared to other mobile manipulation

platforms, more promising for all-terrain applications that

require executing manipulation actions with large physical

interaction or increased payload capacity. This promise has

in no case been fulﬁlled so far since very few works [1]–[8]

have addressed the problem of simultaneously performing

locomotion and manipulation tasks on real quadrupeds.

Among other challenging tasks, quadruped manipulators

promise robotizing heavy payload transportation in non-ﬂat

terrain, a task that is tedious for humans and unsuitable for

their wheeled and aerial counterparts (while it has been also

subject of research for humanoid robots [9]). At the presence

of payload with substantial mass the robot dynamics are

highly affected. As a result, locomoting while simultane-

ously carrying heavy payload poses signiﬁcant challenges to

the robot, namely compromising stability, forcing actuator

saturation and reaching joint limits.

Despite the existence of numerous quadruped manipula-

tors [1]–[3], [10]–[13], their deployment and feasibility to

maintain locomotion while carrying heavy payload (more

This work was supported by the European Union’s Horizon 2020 pro-

gramme under Grant Agreements No. 101016007 (CONCERT) and No.

871237 (SOPHIA).

All authors are with Humanoid and Human-Centered Mechatronics

Research Line, Italian Institute of Technology, Genoa 16163, Italy (emails:

name.surname@iit.it). Ioannis Dadiotis is also with the Depart-

ment of Informatics, Bioengineering, Robotics and Systems Engineering,

University of Genoa, Genoa 16145, Italy.

Fig. 1. The CENTAURO robot walking while carrying 17 kg payload.

Corresponding video: https://youtu.be/09APxzIehpI

than 15 % of the robot’s mass) has been either relatively

unexplored or compromised by generating motions only for

the lower-body of the robot and overlooking the manipulation

capabilities of the platform [14]. Relying solely on loco-

motion for a task involving high interaction forces/payload

at the robot’s upper body can result in inefﬁcient or at

best suboptimal robot behavior. On the contrary, considering

both locomotion and payload manipulation together at the

planning stage is a more sophisticated alternative that can

result in lower-body trajectories of greater margins, which

can be tracked more easily.

This work optimizes both locomotion and manipulation

and considers both robot and payload simpliﬁed model

dynamics together at the level of motion planning (before

control). Deploying payload manipulation results in avoiding

compromising kinematic performance of the robot’s lower-

body and remaining far from leg singular conﬁgurations

in kinematically demanding motions. The formulation is

combined with a whole-body controller (WBC) and the

framework, efﬁciently, generates a variety of motions (for

ﬂat and non-ﬂat terrains) that are successfully executed in

both simulation and real hardware under heavy payload.

A. Related Work

Previous work on CENTAURO [14] relies on total CoM

estimation to plan only lower-body motion (no manipulation

planning) for heavy payload transportation. Reaching the

leg workspace kinematic limits (outstretching) is traded off

with zero moment point (ZMP) stability margin through a

cost term. In contrast, the current approach leverages the

platform’s dual arm manipulation capabilities to avoid leg

arXiv:2210.06803v1 [cs.RO] 13 Oct 2022

outstretching without compromising stability. Indeed, the

framework achieves to plan and execute more challenging

motions on both simulation and real hardware.

Existing works have explored separating locomotion and

manipulation planning. In [1] contact wrenches are com-

manded to the controller while the planner accounts only for

locomotion. Similarly the BigDog robot of Boston Dynamics

[13] was shown to carry and throw a cinder block [4].

The work of [5] proposes a learned locomotion policy

that accounts for the predicted wrenches on the robot base

planned by a separate model-based manipulation planner.

The above approaches suffer from the same drawback in that

locomotion planning is assigned to compensate for/reject the

manipulation motion effect without having control over it.

Thus, the manipulation behavior cannot be changed based

on locomotion margins.

On the other hand locomotion and manipulation have been

simultaneously optimized for bipeds, to name but a few

[15], [16], and more recently for quadruped manipulators

as follows. The full dynamics TO formulations of [8],

[17] have achieved robustness against payloads [18] but are

computationally expensive (prohibiting online planning for a

robot much simpler than the one used in this paper).

The work of [19] substitutes the feet contact forces with

the ZMP for achieving tasks on ﬂat terrain in simulation.

On the contrary, the uniﬁed framework of [6] accounts

for the centroidal robot dynamics and manipulated object

to efﬁciently plan combined locomotion and manipulation

tasks. Although the latter seems to ﬁnd application for the

heavy payload transportation task, scaling efﬁciently1to

more complex robots as the CENTAURO (which consists

of 39 actuated degrees of freedom [DoF] in contrast to

the 16-DoF robot used) remains challenging2. The current

paper handles this complexity by adopting a middle ground

between [19] and [6] in terms of robot model descriptiveness.

It accounts for a model richer than [19] since optimizing for

all contact forces as well as arm end-effectors (EE) motion.

The resulted TO is computationally efﬁcient (planning at

least at 5 Hz with 4 sec. horizon) and is validated on the

real CENTAURO robot, which is of much higher system

dimension than any of the works above. Differently from

other works, results and insight are presented from real

experiments on non-ﬂat terrain with 17 kg payload (85 %

of the arms’ capacity and 15.1 % of the robot mass).

B. Contribution

Based on the current literature, as discussed in I-A, this

work is characterized by the following contributions:

•A TO formulation for motion planning of quadruped

manipulators carrying heavy payload. The formulation

simultaneously plans locomotion and payload manipu-

lation and as a result, in contrast to locomotion-only,

1In this paper, a TO is considered computationally efﬁcient if the planning

time is at least an order of magnitude shorter than the planning horizon.

2This is further compounded since by the time of writing the augmented-

Lagrangian-based inequality constraint handling approach [20] that is used

in [6] is not yet open source released, thus cannot be off-the-shelf accessed.

avoids excessive lower-body motion that can cause leg

outstretching (boundary singularities) when stepping.

•The formulation is used for (but, as shown in Sec. IV-

D, not restricted to) ofﬂine planning. Combined with

a WBC it is evaluated in various simulation and ex-

perimental scenarios with the CENTAURO robot [11],

demonstrating the ability to generate motions that can be

tracked by real robots of high complexity. The obstacles

negotiated in both simulation and real experiment have

not been shown before from a quadruped manipulator

that carries such heavy payload.

•The approach is computationally efﬁcient for high di-

mensional robots (as is a bi-manual quadruped) such

that can be straightforwardly extended to online reced-

ing horizon TO. This work is the ﬁrst to provide insights

on the application and efﬁciency of simpliﬁed model-

based TO on quadrupeds with more than one arms.

II. TRAJECTORY OPTIMIZATION FORMULATION

In this work, the motion planning problem is formulated

using direct transcription/collocation which transcribes the

continuous optimization problem in a constrained Nonlinear

Programming (NLP) problem. This is done by discretizing

the horizon of the optimization in a number of knots and

the solver is assigned to ﬁnd the optimal values of the

variables at these knots. The optimal values of the obtained

solution are then interpolated. Although many off-the-shelf

NLP solvers exist interior-point ones are faster [18], [21] and

can handle any type of constraint, thus, they are preferred.

The TO formulation plans both locomotion and manipula-

tion trajectories for the task of carrying heavy payload with

known mass3, thus referred as payload-aware. It consists of

a CoM and arm EE motion planning framework, i.e. feet

trajectories are not optimized. The latter are, heuristically,

planned before the TO based on user inputs (gait pattern,

stride length and duration, total time Tof the motion and step

vertical clearance). Based on the above, feet EE trajectories

are known and introduced in the TO as NLP parameters.

The robot arms are considered in rigid (prehensile) contact

with the payload and able to manipulate it, thus, the motion

of the payload is identical to the motion of the arm EE. The

CENTAURO robot has two arms and, henceforth, this paper

focuses on scenarios with one payload at each arm. However

the approach can be easily adapted for different quadrupeds.

For the rest of this paper all position vectors are expressed

in a ﬁxed inertial (world) frame whose notation is omitted.

A. Decision variables

The formulation optimizes the CoM state z

z(t) =

r

r(t)˙

r(t)¨

r(t)T, which includes position, velocity and

acceleration vectors, the CoM jerk ...

r(t), the motion of the

arm EEs as well as the forces f

fi(t)at all (feet and arm)

EEs. Fixed-step discretization is used, thus t=k·∆twhere

k∈ {0, ..., N −1}and Nthe number of knots. For the rest

3The mass of a grasped payload can be estimated through force estimation

at the EE using a wrist force/torque sensor or by exploring the joint torque

sensing available on the arm.

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TrajectoryOptimizationforQuadrupedMobileManipulatorsthatCarryHeavyPayloadIoannisDadiotis,ArturoLaurenziandNikosTsagarakis©2022IEEE.Personaluseofthismaterialispermitted.PermissionfromIEEEmustbeobtainedforallotheruses,inanycurrentorfuturemedia,includingreprinting/republishingthismaterialforadvertising...

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Trajectory Optimization for Quadruped Mobile Manipulators that Carry Heavy Payload Ioannis Dadiotis Arturo Laurenzi and Nikos Tsagarakis

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