For robotic arms to operate in arbitrary environments, especially near people, it is critical to certify the safety of their motion planning algorithms. However, there is often a trade-off between safety and real-time performance; one can either carefully design safe plans, or rapidly generate potentially-unsafe plans. This work presents a receding-horizon, real-time trajectory planner with safety guarantees, called ARMTD (Autonomous Reachability-based Manipulator Trajectory Design). The method first computes (offline) a reachable set of parameterized trajectories for each joint of an arm. Each trajectory includes a fail-safe maneuver (braking to a stop). At runtime, in each receding-horizon planning iteration, ARMTD constructs a reachable set of the entire arm in workspace and intersects it with obstacles to generate sub-differentiable and provably-conservative collision-avoidance constraints on the trajectory parameters. ARMTD then performs trajectory optimization for an arbitrary cost function on the parameters, subject to these constraints. On a 6 degree-of-freedom arm, ARMTD outperforms CHOMP in simulation and completes a variety of real-time planning tasks on hardware, all without collisions.
Anterior cruciate ligament (ACL) reconstruction necessitates months of rehabilitation, during which a clinician evaluates whether a patient is ready to return to sports or occupation. Due to their time- and cost-intensive nature, these screenings to assess progress are unavailable to many. This paper introduces an automated, markerless, camera-based method for estimating rehabilitation criteria following ACL reconstruction. To evaluate the performance of this novel technique, data were collected weekly from 12 subjects as they used a leg press over the course of a 12-week rehabilitation period. The proposed camera-based method for estimating displacement and force was compared to encoder and force plate measurements. The leg press displacement and force values were estimated with 89.7% and 85.3% accuracy, respectively. These values were then used to calculate lower-limb symmetry and to track patient progress over time.