High absolute accuracy is an essential prerequisite for a humanoid robot to autonomously and robustly perform manipulation tasks while avoiding obstacles. We present for the first time a kinematic model for a humanoid upper body incorporating joint and transversal elasticities. These elasticities lead to significant deformations due to the robot's own weight, and the resulting model is implicitly defined via a torque equilibrium. We successfully calibrate this model for DLR's humanoid Agile Justin, including all Denavit-Hartenberg parameters and elasticities. The calibration is formulated as a combined least-squares problem with priors and based on measurements of the end effector positions of both arms via an external tracking system. The absolute position error is massively reduced from 21 mm to 3.1 mm on average in the whole workspace. Using this complex and implicit kinematic model in motion planning is challenging. We show that for optimization-based path planning, integrating the iterative solution of the implicit model into the optimization loop leads to an elegant and highly efficient solution. For mildly elastic robots like Agile Justin, there is no performance impact, and even for a simulated highly flexible robot with 20 times higher elasticities, the runtime increases by only 30%.

Planning collision-free motions for robots with many degrees of freedom is challenging in environments with complex obstacle geometries. Recent work introduced the idea of speeding up the planning by encoding prior experience of successful motion plans in a neural network. However, this "neural motion planning" did not scale to complex robots in unseen 3D environments as needed for real-world applications. Here, we introduce "basis point set", well-known in computer vision, to neural motion planning as a modern compact environment encoding enabling efficient supervised training networks that generalize well over diverse 3D worlds. Combined with a new elaborate training scheme, we reach a planning success rate of 100 %. We use the network to predict an educated initial guess for an optimization-based planner (OMP), which quickly converges to a feasible solution, massively outperforming random multi-starts when tested on previously unseen environments. For the DLR humanoid Agile Justin with 19 DoF and in challenging obstacle environments, optimal paths can be generated in 200 ms using only a single CPU core. We also show a first successful real-world experiment based on a high-resolution world model from an integrated 3D sensor.

When a humanoid robot performs a manipulation task, it first makes a model of the world using its visual sensors and then plans the motion of its body in this model. For this, precise calibration of the camera parameters and the kinematic tree is needed. Besides the accuracy of the calibrated model, the calibration process should be fast and self-contained, i.e., no external measurement equipment should be used. Therefore, we extend our prior work on calibrating the elastic upper body of DLR's Agile Justin by now using only its internal head-mounted RGB camera. We use simple visual markers at the ends of the kinematic chain and one in front of the robot, mounted on a pole, to get measurements for the whole kinematic tree. To ensure that the task-relevant cartesian error at the end-effectors is minimized, we introduce virtual noise to fit our imperfect robot model so that the pixel error has a higher weight if the marker is further away from the camera. This correction reduces the cartesian error by more than 20 %, resulting in a final accuracy of 3.9 mm on average and 9.1 mm in the worst case. This way, we achieve the same precision as in our previous work [1], where an external cartesian tracking system was used.