Optimal Control Approach for Non-prehensile Ball Juggling Using a 7-DoF Manipulator

Dynamic object exchange between humans and robots remains a challenging problem due to uncertainty in perception, timing, and contact-rich interaction. Human-robot juggling represents a particularly demanding instance of this problem, requiring precise real-time coordination, predictive motion planning with feedback control, and robustness to variability in human motion. Enabling such skills is of interest for advancing physical human-robot interaction and shared autonomy. We present a real-time planning and control architecture for human-robot partner juggling that enables a robot to reliably catch and throw balls in synchronized multi-ball patterns with a human partner. The system integrates predictive ball tracking, adaptive online trajectory optimization using a multiple-shooting formulation, and a state-machine-based coordination logic to enable synchronized multi-ball human-robot partner juggling. In a user study with 8 participants of varying juggling skill from beginner to expert, we demonstrate that our system can achieve three-ball cascades shared between the robot and the human. All participants exceeded previously reported best-case results within a 10-minute test session, with one participant extending the previous record for shared three-ball cascade juggling fivefold to 20 consecutive robot catches, and another participant achieving a 100% success rate with 40 consecutive catches in a single-ball catch-and-return setting. Video documentation can be found at https://kai-ploeger.com/partner-juggling

Robotic throwing enables fast object transport and extends a robot's reachable workspace beyond traditional pick-and-place. While prehensile (grasp-based) throwing works well for graspable items, non-prehensile (grasp-free) throwing is better suited for large, heavy, and/or deformable objects. Existing approaches rely on model-based optimization with simplified contact models (e.g., dynamic grasping) and low-dimensional trajectory parameterizations, which limit solution quality and reachable workspace. We propose a reinforcement learning approach that additionally leverages sliding and rolling contact modes and directly optimizes joint-space trajectories without analytical contact models or custom parameterizations. The Markov Decision Process (MDP) is formulated as a dynamical system that evolves the robot's joint state conditioned on the throwing target, object model, and initial configuration. Joint-jerk trajectories are planned offline at a low control rate and upsampled into smooth, high-rate velocity commands for deployment. For sim-to-real transfer, we minimize the robot-dynamics gap through minimum-jerk system identification and train uncertainty-aware policies to mitigate object-modeling errors, particularly sensitivity to dynamic friction. In simulation, the policy achieves 99% success across thousands of configurations and generalizes to unseen objects. Sensitivity analysis shows robustness to mass uncertainty but high sensitivity to dynamic friction, consistent with the sliding-based release mechanism. Deployed zero-shot on a UR5e operating near its physical limits (5 m/s end-effector velocity), our method throws diverse objects including heavy (790 g) and large (20x20x28 cm) items to targets up to 350 cm distance or 180 cm elevation, achieving a 97% real-world success rate.

For residual learning that refines existing behavior, sample efficiency depends on two things: how much information each rollout returns, and how efficiently the learner uses that information. Reinforcement learning's standard scalar reward carries far less information than the directional task error that defines the task. Random exploration further discards whatever information each rollout returns. Through residual learning with directional task-error supervision and a task error model that drives sample selection, we achieve stable three-, four-, and five-ball juggling on anthropomorphic Barrett WAM arms. Despite planning and controlling through a simple, idealized stack, the system converges from the second attempt. The first attempt drops, after which task error decreases monotonically without further failures. In comparison, five-ball juggling typically takes humans years of practice. We compare residual learners across two ternary axes, the directional information in the learning feedback and the commitment of the analytic prior, spanning Newton-style Jacobian updates, Composite Bayesian Optimization, and stochastic search methods. Both axes prove necessary: neither directional feedback nor an informative prior suffices alone, and the simplest method that combines them, a fixed-Jacobian Newton update, is the most reliable. The learned residual tolerates substantial prior misalignment and degraded joint tracking, affecting mainly convergence speed. The bottleneck for residual learning on real robots is therefore the information content of the supervision signal and how the learner uses it, not the accuracy of the surrounding stack. Video documentation of all experiments is available at https://kai-ploeger.com/residual-juggling.