Precision Jumping with a SLIP-like Robot filePrecision Jumping with a SLIP-like Robot Justin K. Yim...
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Precision Jumping with a SLIP-like Robot Justin K. Yim 1 and Ronald S. Fearing 1 Abstract—We developed a deadbeat foot placement hopping controller for an untethered monopedal robot, Salto-1P. The controller uses a third order Taylor series approximation to an offline SLIP-like dynamic model and performs well on the physical platform. Due to the robot’s similarity to the SLIP template, control is based closely on the SLIP-like model without adjustment required for the physical platform. We found that the SLIP-like model’s horizontal velocity at takeoff becomes more sensitive to the touchdown leg angle as the hopping height increases. I. INTRODUCTION We consider a SLIP-like hopping model to develop dead- beat foot placement hopping control in which the robot can place its foot at a desired foothold point after only one intervening stance phase. During flight, a jumping robot has no control over the motion of its center of gravity (CG) without specialized means to apply large forces in the air. To reach a desired foothold, the robot must set its velocity at takeoff to aim its flight path towards the foothold. A SLIP-like robot’s takeoff velocity can be changed by setting stance initial conditions like leg angles at the previous flight’s touchdown as in [2]. In [1] we demonstrated that this is effective for robots like Salto-1P with short stances and high accelerations. II. METHODS In order to predict takeoff velocities resulting from certain touchdown conditions, we simulated stance in a Matlab rigid body simulation matched to the physical parameters of Salto- 1P. Salto-1P’s mechanics are very similar to the SLIP-model, leading to the following simplifications. Salto-1P’s moment of inertia about its lateral and longitu- dinal axes are both approximately 130 × 10 -6 kg m 2 . Since the robot weighs 0.103 kg and its CG is 0.10 m above its foot with the leg fully retracted, the robot’s moment of inertia about its foot is dominated by the CG distance from the foot and is not significantly changed by the robot body’s heading. Since the robot’s foot moves along a straight line coincident with the CG and its moment of inertia is nearly the same at all headings, the robot’s stance phase is insensitive to heading and its touchdown yaw angle can be neglected. This material is based upon work supported by the United States Army Research Laboratory under the Micro Autonomous Science and Technology Collaborative Technology Alliance and the Army Research Office Grant No. W911NF-18-1-0038. 1 J.K. Yim, and R.S. Fearing are with the Department of Elec- trical Engineering and Computer Sciences, University of Califor- nia, Berkeley, CA 94720 USA [email protected], [email protected] Fig. 1. Salto-1P’s CG-dominated inertia and straight-line foot motion make it very similar to the SLIP template and enable direct application of a controller derived from simple models on the physical platform. Furthermore, since the balanced inertial tail’s angular velocity is kept low by braking during stance phase, the tail’s angular momentum is small compared to the angular momentum due to the motion of the robot’s CG. As with the robot’s yaw heading, the tail angle and angular velocity are also neglected. With the above assumptions, the robot’s behavior is similar to a SLIP-like point mass and motor- controlled leg force. Since neither this SLIP-like model nor the canonical SLIP model has a closed form solution, we numerically simulated stance trajectories for 16,170 initial conditions. The robot’s control actions are selected using a third order polynomial curve fit to these offline simulation results. III. RESULTS Since Salto-1P behaves very similarly to the SLIP-like model, no modifications to the controller were required for operation on the physical robot. We demonstrated that the controller’s foot placement accuracy with the physical robot is high enough that the robot can jump up onto a chair and desk and then back down as shown in Fig. 2. As in Raibert’s early hopping control work [2], Salto-1P’s takeoff horizontal velocity is highly sensitive to touchdown leg angle. In this work, we found that this sensitivity of takeoff horizontal velocity to touchdown leg angle increases as the robot’s vertical velocity increases as shown in Fig. 3. This means that a given touchdown leg angle error will Workshop on Modeling and Control of Dynamic Legged Locomotion: Insights from Template (Simplified) Models IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2018, Madrid, Spain
Transcript of Precision Jumping with a SLIP-like Robot filePrecision Jumping with a SLIP-like Robot Justin K. Yim...
Precision Jumping with a SLIP-like Robot
Justin K. Yim1 and Ronald S. Fearing1
Abstract— We developed a deadbeat foot placement hoppingcontroller for an untethered monopedal robot, Salto-1P. Thecontroller uses a third order Taylor series approximation toan offline SLIP-like dynamic model and performs well onthe physical platform. Due to the robot’s similarity to theSLIP template, control is based closely on the SLIP-like modelwithout adjustment required for the physical platform. Wefound that the SLIP-like model’s horizontal velocity at takeoffbecomes more sensitive to the touchdown leg angle as thehopping height increases.
I. INTRODUCTION
We consider a SLIP-like hopping model to develop dead-beat foot placement hopping control in which the robot canplace its foot at a desired foothold point after only oneintervening stance phase.
During flight, a jumping robot has no control over themotion of its center of gravity (CG) without specializedmeans to apply large forces in the air. To reach a desiredfoothold, the robot must set its velocity at takeoff to aim itsflight path towards the foothold. A SLIP-like robot’s takeoffvelocity can be changed by setting stance initial conditionslike leg angles at the previous flight’s touchdown as in [2].In [1] we demonstrated that this is effective for robots likeSalto-1P with short stances and high accelerations.
II. METHODS
In order to predict takeoff velocities resulting from certaintouchdown conditions, we simulated stance in a Matlab rigidbody simulation matched to the physical parameters of Salto-1P. Salto-1P’s mechanics are very similar to the SLIP-model,leading to the following simplifications.
Salto-1P’s moment of inertia about its lateral and longitu-dinal axes are both approximately 130× 10−6 kg m2. Sincethe robot weighs 0.103 kg and its CG is 0.10 m above itsfoot with the leg fully retracted, the robot’s moment of inertiaabout its foot is dominated by the CG distance from the footand is not significantly changed by the robot body’s heading.Since the robot’s foot moves along a straight line coincidentwith the CG and its moment of inertia is nearly the same atall headings, the robot’s stance phase is insensitive to headingand its touchdown yaw angle can be neglected.
This material is based upon work supported by the United States ArmyResearch Laboratory under the Micro Autonomous Science and TechnologyCollaborative Technology Alliance and the Army Research Office Grant No.W911NF-18-1-0038.
1J.K. Yim, and R.S. Fearing are with the Department of Elec-trical Engineering and Computer Sciences, University of Califor-nia, Berkeley, CA 94720 USA [email protected],[email protected]
Fig. 1. Salto-1P’s CG-dominated inertia and straight-line footmotion make it very similar to the SLIP template and enabledirect application of a controller derived from simple models onthe physical platform.
Furthermore, since the balanced inertial tail’s angularvelocity is kept low by braking during stance phase, thetail’s angular momentum is small compared to the angularmomentum due to the motion of the robot’s CG. As withthe robot’s yaw heading, the tail angle and angular velocityare also neglected. With the above assumptions, the robot’sbehavior is similar to a SLIP-like point mass and motor-controlled leg force.
Since neither this SLIP-like model nor the canonical SLIPmodel has a closed form solution, we numerically simulatedstance trajectories for 16,170 initial conditions. The robot’scontrol actions are selected using a third order polynomialcurve fit to these offline simulation results.
III. RESULTS
Since Salto-1P behaves very similarly to the SLIP-likemodel, no modifications to the controller were required foroperation on the physical robot. We demonstrated that thecontroller’s foot placement accuracy with the physical robotis high enough that the robot can jump up onto a chair anddesk and then back down as shown in Fig. 2.
As in Raibert’s early hopping control work [2], Salto-1P’stakeoff horizontal velocity is highly sensitive to touchdownleg angle. In this work, we found that this sensitivity oftakeoff horizontal velocity to touchdown leg angle increasesas the robot’s vertical velocity increases as shown in Fig.3. This means that a given touchdown leg angle error will
Workshop on Modeling and Control of Dynamic Legged Locomotion: Insights from Template (Simplified) ModelsIEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2018, Madrid, Spain
produce larger and larger horizontal velocity errors as therobot’s vertical velocity and hopping height increase. Asa result, the robot’s touchdown leg angle must be moreaccurate as the hopping height increases if it is not to missits foothold.
Fig. 2. Salto-1P jumps up onto a chair and desk (trajectory in blue),then back down (not shown). The chair seat is 0.44 m high and thedesk is 0.71 m high. The robot is 0.32 m tall with its leg extendedto its maximum length of 0.15 m.
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Fig. 3. Takeoff horizontal velocity vox sensitivity to leg angle θincreases with increasing vertical velocity (equivalent to increasinghopping height).
REFERENCES
[1] D. W. Haldane, J. K. Yim, and R. S. Fearing, “Repetitive extreme-acceleration ( 14-g ) spatial jumping with Salto-1P,” IEEE Int. Conf.Intell. Robots. Syst., pp. 3345–3351, 2017.
[2] M. H. Raibert and J. H. B. Brown, “Experiments in Balance Witha 3D One-Legged Hopping Machine,” Journal of Dynamic Systems,Measurement, and Control, vol. 106, no. 1, pp. 75–81, 1984. [Online].Available: http://dx.doi.org/10.1115/1.3149668
Workshop on Modeling and Control of Dynamic Legged Locomotion: Insights from Template (Simplified) ModelsIEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2018, Madrid, Spain
