Minimizing energy in hexapod

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Advanced Robotics 23 (2009) 681–704

Full paper
Minimizing Energy Consumption in Hexapod Robots
P. Gonzalez de Santos ∗ , E. Garcia, R. Ponticelli and M. Armada
Institute of Industrial Automation — CSIC, Department of Automatic Control, Ctra. Campo Real
Km 0,2, 28500 Arganda del Rey, Madrid, Spain
Received 15 July 2008; revised 25 November 2008; accepted 3 December 2008Abstract
Minimization of energy expenditure in autonomous mobile robots for industrial and service applications is
a topic of huge importance, as it is the best way of lengthening mission time without modifying the power
supply. This paper presents a method to minimize the energy consumption of a hexapod robot on irregular
terrain. An energy-consumption model is derived for staticallystable gaits before applying minimization
criteria. Then, some parameters that define the foot trajectories of the legged robot are computed to minimize energy expenditure during every half a locomotion cycle. The method is evaluated using an accurate
geometric model of the SILO-6 walking robot.
© Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2009
Energy efficiency, energyconsumption, legged locomotion, mobile robots, optimization methods

1. Introduction
An autonomous mobile robot is an intelligent machine with the skills to perform
motion in an unstructured environment without explicit human intervention. Its
intelligent autonomy is provided by efficient algorithms capable of coping with
many different situations. Nevertheless, a real-application autonomousrobot must
also exhibit energy autonomy; the greater the autonomy, the better. Both sorts of
autonomies are required for real operative mobile robots. Intelligent autonomy is
provided by sensors and algorithms. Energy autonomy is mainly accomplished using efficient power supplies. However, the control algorithms that mobile robots use
can help lengthen the duty cycle of power supplies and soextend the robot’s operation time. This is especially significant in legged locomotion (both multi-legged and
biped robots), which can move along a given path with many different leg and body
poses and, thus, with many different energy expenditure rates. Even though multi*

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© Koninklijke Brill NV, Leiden and The RoboticsSociety of Japan, 2009



P. Gonzalez de Santos et al. / Advanced Robotics 23 (2009) 681–704

legged and biped robots exhibit many different features, they can share common
energy optimization criteria [1], as presented below.
Different approaches to the energy efficiency of multi-legged robots have been
studied. Some results have been obtained from thegait-parameter standpoint alone
[2]. However, such models are extremely simplified, and do not consider the forces
and torques involved in the process, which must be factored into energy computations. Early work for minimizing power consumption considered the actuator
dynamics [3]; however, the theory was applied to hydraulic actuators, while we are
interested in DC motors. Afterwards, Nahon andAngeles [4] worked on minimizing the power of robotic systems with DC motors, but allowed power regeneration
by motors performing negative work; this capability is not offered by current technology. Later, Marhefka and Orin studied the force distribution problem in walking
robots that minimizes the power consumption in DC motors disabling regeneration
of negative work [5]. These results werethen used to minimize the total power
along a locomotion cycle rather than at one given instant [6]. There are other authors that have taken into account leg dynamics and torques [7–9] but they have still
failed to consider joint actuator type, although the joint actuator’s contribution to
energy consumption is decisive. Additionally, they focused their works on walking
locomotion over flat...
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