Hi there, in the recent years there has been a lot of progress concerning deep reinforcement learning and many publications are available that prove that machine learning can create stable gaits for robots. Mainly interesting and relatively understandable papers are for example https://arxiv.org/abs/1804.10332, where the authors created a walking and also a galloping gait based on training in simulation and a later application on the robot. In a later publication they further advanced and made it possible to learn new gaits via reinforcement directly on the robot without simulation in less than 2 hours https://arxiv.org/abs/1812.11103 There are a lot more examples and different approaches to this. Nevertheless, this is very remarkable and this made me thinking, whether we can get there also with Nybble and Bittle. But let's slow down a little. What's reinforcement learning in particular? When you look at the graph below you can get a basic understanding how this works: The Agent, in our case Nybble/Bittle is set in an Environment (e.g. flat floor). There it performs Actions like moving the limbs somehow and trying to get a Reward from the Programmer. The Reward is only given when the State is what we actually want, e.g. moving forward. Trapped in this loop our robot will try to maximize the Reward in every iteration becoming better and better in the movement. Source: https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg So what I tried to do now, is to use a simulation environment with a flat ground together with a simulation model of Nybble and wanted to make it move forward. I implemented this in the gym training environment in PyBullet with the reinforcement library Stable-Baselines3 https://stable-baselines3.readthedocs.io/en/master/index.html# . There are a lot of functional learning algorithms one can use for reinforcement learning. So for training in my case I tried an algorithm called SAC (Soft Actor-Critic) that seems to be the current state-of-the-art algorithm for reinforcement learning and applied it on Nybble to see how it performs. And the results is definitely still more a crawling than a walking gait, but it shows the potential. This is a result of reinforcement training only without any intervention from my side: The next steps are to improve training and the resulting gaits. And once the gaits are good in simulation there are two ways. One is trying to get the learning policy running on Nybble/Bittle or learn it directly on them. I think there I have to use an additional set of hardware to make it run. If you want to train a walking gait, you can find the link to my repository below, where I will provide further updates. Make sure to install all the necessary python libraries in the import section of the code. https://github.com/ger01d/opencat-gym

Hi there, a few weeks ago I've been working on the kinematic modeling of Nybble and was deriving gaits like walking climbing etc. with this method (see the other post "Kinematic Model"). The problem was, that without further physical description, the kinematic model is to idealistic. Normally Nybble shifts its weight and there will be some kind of momentum leading to unpredictable movements. Therefore I concentrated on extending the kinematic model with a physical description in a simulation environment called pybullet. So first, let's take a look at the result: The model is based on an URDF File (Unified Robotics Description Format) which is a common file format that can be implemented in different simulation environments. Please take a closer look at the attached URDF-file for more information. It's mostly self explanatory. One Note: Masses, inertia, friction damping and so on are a first estimation and certainly not correct. If you have better data, please update the information in the URDF-file and upload it to the forum. I copied the walking gait from the instincts.h into the environment and controlled the position of the joints and links to make Nybble walk. This makes it interesting to test new gaits before implementing it on Nybble and creates many more possibilities. To make it run, you will have to install pybullet via python pip and also the bullet environment. Please see the homepage for further details: https://pybullet.org/wordpress/ Here's the code for the pybullet simulation: And this is the necessary URDF-file: (Please rename to nybble.urdf.I couldn't upload it with an URDF ending.) I will provide further code updates on: https://github.com/ger01d/dynamic-model-opencat

Creating gaits, especially walking, trotting etc. is quite a challenging task, if you do this manually. It is therefore favorable to have a kinematic model of our cat. I wanted to show you my approach to create a new gait via Inverse Kinematics, where I'm using the IKPY library (https://github.com/Phylliade/ikpy). Inverse kinematics at a glance is that you provide a point in space and the angles of the motors are calculated. In IKPY this is achieved by creating "chains" e.g. upper_arm--lower_arm--paw. Then you decide where to place the paw in space. Below you can see an image of Nybbles Kinematic model, to give you a first impression. For the first tests I created an alternative walking gait that follows as swing-stance-pattern of this form: # Walking pattern (1 == swing) # [0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 1,1,1,1,1], # LL # [0,0,0,0,0, 1,1,1,1,1, 0,0,0,0,0, 0,0,0,0,0], # RL # [0,0,0,0,0, 0,0,0,0,0, 1,1,1,1,1, 0,0,0,0,0], # LA # [1,1,1,1,1, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0], # RA The longitudinal movement (blue) and the lift (orange) is based on sine/cosine-functions, that follow the pattern phase shift as shown above. This pattern in combination with the IK-model will lead to this movement: I also tried this new gait on Nybble for validation and it works quite well. The lift is 1 cm in amplitude, so Nybble can now step over a small obstacle. Further updates and the Bittle-Version can be found here: https://github.com/ger01d/kinematic-model-opencat So here's the code for the version above: import ikpy from ikpy.chain import Chain from ikpy.link import OriginLink, URDFLink import numpy as np from numpy import sin, cos, pi import matplotlib.pyplot as plt import mpl_toolkits.mplot3d.axes3d as p3 deg2rad = pi/180 # Values in cm armLength = 5 bodyLength = 12 bodyWidth = 10 distanceFloor = 7 stepLength = 5 swingHeight = 1 leanLeft = 0 # Not working, yet leanRight = -leanLeft # Not working, yet leanForward = 0 # cm left_arm = Chain(name='left_arm', links=[ URDFLink( name="center", translation_vector=[leanForward, 0, distanceFloor], orientation=[0, 0, 0], rotation=[0, 0, 0], ), URDFLink( name="shoulder", translation_vector=[0, bodyWidth/2, leanLeft], orientation=[0, 0, 0], rotation=[0, 1, 0], bounds=(0.1*deg2rad, 179*deg2rad), ), URDFLink( name="upperArm", translation_vector=[armLength, 0, 0 ], orientation=[0, 0, 0], rotation=[0, 1, 0], bounds=(-179*deg2rad, -0.1*deg2rad), ), URDFLink( name="lowerArm", translation_vector=[armLength, 0, 0], orientation=[0, 0, 0], rotation=[0, 0, 0], ) ]) right_arm = Chain(name='right_arm', links=[ URDFLink( name="center", translation_vector=[leanForward, 0, distanceFloor], orientation=[0, 0, 0], rotation=[0, 0, 0], ), URDFLink( name="shoulder", translation_vector=[0, -bodyWidth/2, leanRight], orientation=[0, 0, 0], rotation=[0, 1, 0], bounds=(0.1*deg2rad, 179*deg2rad), ), URDFLink( name="upperArm", translation_vector=[armLength, 0, 0], orientation=[0,0,0], rotation=[0,1,0], bounds=(-179*deg2rad, -1*deg2rad), ), URDFLink( name="lowerArm", translation_vector=[armLength, 0, 0 ], orientation=[0,0,0], rotation=[0, 1, 0], ) ]) left_leg = Chain(name='left_leg', links=[ URDFLink( name="center", translation_vector=[leanForward, 0, distanceFloor], orientation=[0, 0, 0], rotation=[0, 0, 0], ), URDFLink( name="butt", translation_vector=[-bodyLength, 0, 0], orientation=[0, 0, 0], rotation=[0, 0, 0], ), URDFLink( name="hip", translation_vector=[0, bodyWidth/2, leanLeft], orientation=[0, 0, 0], rotation=[0, 1, 0], bounds=(0.1*deg2rad, 100*deg2rad), ), URDFLink( name="upperLeg", translation_vector=[armLength, 0, 0 ], orientation=[0, 0, 0], rotation=[0, 1, 0], bounds=(1*deg2rad, 179*deg2rad), ), URDFLink( name="lowerLeg", translation_vector=[armLength, 0, 0 ], orientation=[0, 0, 0], rotation=[0, 1, 0], ) ]) right_leg = Chain(name='right_leg', links=[ URDFLink( name="center", translation_vector=[leanForward, 0, distanceFloor], orientation=[0, 0, 0], rotation=[0, 0, 0], ), URDFLink( name="butt", translation_vector=[-bodyLength, 0, 0], orientation=[0, 0, 0], rotation=[0, 0, 0], ), URDFLink( name="hip", translation_vector=[ 0, -bodyWidth/2, leanRight], orientation=[0, 0, 0], rotation=[0, 1, 0], bounds=(0.1*deg2rad, 100*deg2rad), ), URDFLink( name="upperLeg", translation_vector=[armLength, 0, 0 ], orientation=[0, 0, 0], rotation=[0, 1, 0], bounds=(1*deg2rad, 179*deg2rad), ), URDFLink( name="lowerLeg", translation_vector=[armLength, 0, 0], orientation=[0, 0, 0], rotation=[0, 1, 0], ) ]) def buildGait(frames): frame = np.arange(0,frames) swingEnd = pi/2 # longitudinalMovement swing = -cos(2*(frame*2*pi/frames)) stance = cos(2/3*(frame*2*pi/frames-swingEnd)) swingSlice = np.less_equal(frame,swingEnd/(2*pi/frames)) stanceSlice = np.invert(swingSlice) longitudinalMovement = np.concatenate((swing[swingSlice], stance[stanceSlice])) longitudinalMovement = np.concatenate((longitudinalMovement,longitudinalMovement,longitudinalMovement, longitudinalMovement)) # verticalMovement lift = sin(2*(frame*2*pi/frames)) liftSlice = swingSlice verticalMovement = np.concatenate((lift[liftSlice], np.zeros(np.count_nonzero(stanceSlice)))) verticalMovement = np.concatenate((verticalMovement, verticalMovement, verticalMovement, verticalMovement)) return longitudinalMovement, verticalMovement frames = 43 longitudinalMovement, verticalMovement = buildGait(frames) # Walking pattern # [0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 1,1,1,1,1], # LL # [0,0,0,0,0, 1,1,1,1,1, 0,0,0,0,0, 0,0,0,0,0], # RL # [0,0,0,0,0, 0,0,0,0,0, 1,1,1,1,1, 0,0,0,0,0], # LA # [1,1,1,1,1, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0], # RA # Phase shift between arms/legs, [RA, RL, LA, LL] shiftFrame = np.round(np.array([0, pi/2, pi, 3*pi/2])/2/pi*frames) shiftFrame = shiftFrame.astype(int) for frame in range(0, frames): right_arm_angles = 180/pi*right_arm.inverse_kinematics(target_position = np.array([stepLength*longitudinalMovement[frame], -bodyWidth/2 ,swingHeight*verticalMovement[frame]])) right_arm_correction = np.array([0, -90, 90, 0]) right_arm_angles = np.round(right_arm_angles+right_arm_correction) right_arm_angles = np.delete(right_arm_angles, np.s_[0,3], axis=0) right_arm_angles = right_arm_angles.astype(int) right_leg_angles = 180/pi*right_leg.inverse_kinematics(target_position = np.array([-bodyLength+stepLength*longitudinalMovement[frame+shiftFrame[1]], -bodyWidth/2 , swingHeight*verticalMovement[frame+shiftFrame[1]]])) right_leg_correction = np.array([0, 0, -90, -90, 0]) right_leg_angles = np.round(right_leg_angles+right_leg_correction) right_leg_angles = np.delete(right_leg_angles, np.s_[0,1,4], axis=0) right_leg_angles = right_leg_angles.astype(int) left_arm_angles = 180/pi*left_arm.inverse_kinematics(target_position = np.array([stepLength*longitudinalMovement[frame+shiftFrame[2]], +bodyWidth/2 , swingHeight*verticalMovement[frame+shiftFrame[2]]])) left_arm_correction = np.array([0, -90, 90, 0]) left_arm_angles = np.round(left_arm_angles+left_arm_correction) left_arm_angles = np.delete(left_arm_angles, np.s_[0,3], axis=0) left_arm_angles = left_arm_angles.astype(int) left_leg_angles = 180/pi*left_leg.inverse_kinematics(target_position = np.array([-bodyLength+stepLength*longitudinalMovement[frame+shiftFrame[3]], +bodyWidth/2 , swingHeight*verticalMovement[frame+shiftFrame[3]]])) left_leg_correction = np.array([0, 0, -90, -90, 0]) left_leg_angles = np.round(left_leg_angles+left_leg_correction) left_leg_angles = np.delete(left_leg_angles, np.s_[0,1,4],axis=0) left_leg_angles = left_leg_angles.astype(int) # Writing sequence to file gait_sequence = np.concatenate((left_arm_angles, right_arm_angles, right_leg_angles, left_leg_angles)) print(frame," ",gait_sequence) f = open("gait_sequence.csv", "a") f.write("#") np.savetxt(f, gait_sequence[[0,2,4,6,1,3,5,7]], fmt='%3.1i', delimiter=',', newline=", ") f.write("+") f.write("\n") f.close() # Create plot and image for each frame fig = plt.figure() ax = p3.Axes3D(fig) ax.set_box_aspect([3, 3/2,1]) ax.set_xlim3d([-20, 10]) ax.set_xlabel('X') ax.set_ylim3d([-10, 10]) ax.set_ylabel('Y') ax.set_zlim3d([0.0, 10]) ax.set_zlabel('Z') right_arm.plot(right_arm.inverse_kinematics(target_position = np.array([stepLength*longitudinalMovement[frame], -bodyWidth/2 ,swingHeight*verticalMovement[frame]])), ax) right_leg.plot(right_leg.inverse_kinematics(target_position = np.array([-bodyLength+stepLength*longitudinalMovement[frame+shiftFrame[1]], -bodyWidth/2 , swingHeight*verticalMovement[frame+shiftFrame[1]]])), ax) left_arm.plot(left_arm.inverse_kinematics(target_position = np.array([stepLength*longitudinalMovement[frame+shiftFrame[2]], +bodyWidth/2 , swingHeight*verticalMovement[frame+shiftFrame[2]]])), ax) left_leg.plot(left_leg.inverse_kinematics(target_position = np.array([-bodyLength+stepLength*longitudinalMovement[frame+shiftFrame[3]], +bodyWidth/2 , swingHeight*verticalMovement[frame+shiftFrame[3]]])), ax) figureName = "Nybble_" + str(frame) plt.savefig(figureName) #plt.show()