Thermally Constrained Motor Operation for a Climbing RobotSalomon Trujillo and Mark CutkoskyCenter for Design ResearchStanford UniversityStanford, CA 94305–2232, USAEmail: email@example.comAbstract— Climbing robots are especially susceptible to thermaloverload during normal operation, due to the need to opposegravity and to frequently apply internal forces for clinging.As an alternative to setting conservative limits on the motorpeak and average current, we investigate methods for measuringmotor temperatures, predicting motor thermal conditions andgenerating thermally constrained behavior. A thermal model,verified using empirical data, predicts the motor’s windingtemperature based on measured case temperature and inputcurrent. We also present a control strategy that maximizesrobot velocity while satisfying a constraint on the maximumpermissible motor winding temperature.I. INTRODUCTIONClimbing robots are hard on motors. In comparison torobots that walk or run over the ground, climbing robots havehigher average power requirements due to the need to propelthe body vertically in opposition to gravity. In addition, theytypically apply significant internal forces between opposinglimbs to maintain a grip on the climbing surface and preventslippage. At the same time, the motors used in these robotsshould be as light as possible, to help reduce the total weight.These requirements conspire to make motor failure an everpresentdanger when robots attempt to climb rapidly.To combat this danger, a partial solution is to use parallelkinematic chains for the legs and/or power transmissionsystems with differentials, so that more than one motor cancontribute to the required torque for each degree of freedom. Even so, the motors are in danger of being overloadedat increased speed or when a strong grip force is required,for example, to scale a tree or a telephone pole.The primary failure mode of motor overload is overheatingof the windings. Commonly, maximum values are set forthe short term and continuous torque to avoid damagingthe motor. The alternative approach taken in this paper isto construct an empirically validated thermal model of themotors and to use this model in a control scheme that seeksto maximize the vertical speed while keeping the motorwindings below the maximum permissible temperature.Using a commercial low-inertia DC servo motor with abasket-wound rotor (commonly used in robots and hapticinterfaces), we describe the motor thermal model and presentempirical calibration data. We then consider how to specifythe desired torque profile and gait with such motors inthe context of a climbing robot. The robot chosen for thiswork is a variant of the RiSE robot  shown in Fig. 1,which has been configured with four legs instead of theFig. 1. Four-legged variant of the RiSE robot climbing a tree. The frontlegs are in swing while the rear legs are in two-legged stance.usual six. Each leg has two degrees of freedom, driven bya pair of motors through a differential. Passive complianceand damping in each leg help to distribute the forces whenthe legs are gripping. In comparison to the conventionalapproach of specifying a limiting peak and average torque,the explicit thermal control scheme permits faster climbingwithout damaging the motors.II. TEMPERATURE MEASUREMENT ANDPREDICTIONFor a basket-wound coreless DC motor, the most likelythermal failure point is the thin wire used for the rotorwindings . Thus, in order to drive the motor to its thermallimits, a measurement or accurate estimate of the windingtemperature is required. This section presents a thermalmodel that can estimate the winding temperature in shortandlong-term operation as well as the measurement methodused to verify the model.A. Thermal Model of the MotorWe predict the winding temperature using a simple lumpedparameter thermal model, shown in Fig. 2, a method often
Motor Case Temperature ( ° C)60555045403530250 10 20 30Time (Minutes)Allowable climbingduration (Minutes)201510503 4 5 6 7Input power (Watts)Fig. 12. The allowable time spent at each level of power dissipation. Thisdata was recorded at 17 ◦ -20 ◦ C using “A” motors mounted on RiSE.of the windings is long enough that the robot has ampleopportunity to reduce speed and dissipate the extra heat.E. Climbing DurationAs noted in II-E, the motor thermal properties are independentof whether is spinning or stationary. Therefore, tests ona stationary motor exerting torque will yield an estimate ofthe maximum climbing time subject to thermal constraints.By applying a constant current to provide the power specifiedby (3), the outer case heats until the constaint given by(8) is violated. These tests essentially indicate the effectsof ambient temperature and heat conduction into the robotchassis.At 17 ◦ –20 ◦ C ambient temperature, the robot is able todissipate around 3–3.25 watts indefinitely; however, ourslowest presented speed is 3.3 cm/sec which produces 4watts of heat. As shown in Fig. 12, this speed allows forapproximately 8–12 minutes of climbing. At the maximumtested speed in Figs. 9-11, the robot produces 6.4 watts andcould climb for around 2 minutes before having to reducespeed.IV. CONCLUSIONSWe have described an approach to regulating the temperatureof direct current motors for a vertically climbing robotbased on predictions from a thermal model. To empiricallyvalidate the simple lumped-parameter thermal model, we firstconducted experiments on an isolated motor using a noncontactinfrared temperature measurement of the windingsand a surface-mount thermistor on the motor case. Weestablished that by measuring the input current and motorcase temperature, winding temperature can be estimatedindependent of changing ambient conditions.We then explored the effects of a symmetric boundingclimbing gait on the thermal capacity of the motor. Heatdissipation is reduced when forces are distributed amongseveral actuators, suggesting that the duration of the noncontactswing phases should be minimized. However, sincethe swing phase has a minimum duration constrained bysystem friction and available supply voltage, increasing robotvelocity has the effect of decreasing the average number oflegs in contact and thus increases motor heating.Initially, the maximum velocity is thermally unconstrainedas the motor windings are not at their maximum permissibletemperature. Once the temperature limit is reached (after afew minutes in the case of the RiSE robot) climbing velocityis restricted such that the heat dissipated by the windingsequals the mean heat generated. 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